{"id":10689,"date":"2023-12-13T11:37:50","date_gmt":"2023-12-13T06:07:50","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=10689"},"modified":"2023-12-14T16:40:10","modified_gmt":"2023-12-14T11:10:10","slug":"envision-math-common-core-grade-4-answer-key-topic-15","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-15\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement<\/h2>\n

Essential Questions:<\/strong>
\nWhat are some common geometric terms? How can you measure angles?
\n\"Envision<\/p>\n

enVision STEM Project: Lines and Angles<\/strong>
\nDo Research Use the Internet or other sources to research the area of the world’s largest bumper car floor. Find where it is located and when it was built.
\nJournal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Draw a diagram of a bumper car collision. Use an angle to show how a car might change direction after it collides with something. Measure and label the angle you drew.<\/li>\n
  • Describe your angle using some of the vocabulary terms in this topic.<\/li>\n<\/ul>\n

    Review What You Know<\/strong><\/p>\n

    Vocabulary<\/strong><\/p>\n

    Choose the best term from the box. Write it on the blank.<\/p>\n

      \n
    • angle<\/li>\n
    • right angle<\/li>\n
    • line<\/li>\n
    • sixth<\/li>\n<\/ul>\n

      Question 1.
      \nA(n) _________ is one of 6 equal parts of a whole, written as \\(\\frac{1}{6}\\).
      \nAnswer: A\u00a0sixth<\/strong> is one of 6 equal parts of a whole, written as \\(\\frac{1}{6}\\).<\/p>\n

      Question 2.
      \nA(n) _________ is a figure formed by two rays that share the same endpoint.
      \nAnswer: An angle<\/strong> is a figure formed by two rays that share the same endpoint.<\/p>\n

      \"Geometric<\/p>\n

      Question 3.
      \nA(n) ___________ is an angle that forms a square corner.
      \nAnswer: A right angle is an angle that forms a square corner.<\/p>\n

      Adding and Subtracting<\/strong><\/p>\n

      Find the sum or difference.
      \nQuestion 4.
      \n45 + 90
      \nAnswer:
      \nGiven the two numbers 45 and 90
      \nWe have to find the sum of 45, 90.
      \nThe sum of 45 + 90 = 135.<\/p>\n

      Question 5.
      \n120 \u2013 45
      \nAnswer:
      \nGiven the two numbers 120 and 45
      \nWe have to find the difference of 120, 45.
      \nThe difference of 120 – 45 = 75.<\/p>\n

      Question 6.
      \n30 + 150
      \nAnswer:
      \nGiven the two numbers 30 and 150
      \nWe have to find the sum of 30, 150.
      \nThe sum of 30 + 150 = 180.<\/p>\n

      Question 7.
      \n180 \u2013 135
      \nAnswer:
      \nGiven the two numbers 180 and 135
      \nWe have to find the difference of 180, 135.
      \nThe difference of 180 – 135 = 45.<\/p>\n

      Question 8.
      \n60 + 120
      \nAnswer:
      \nGiven the two numbers 60 and 120
      \nWe have to find the sum of 60, 120.
      \nThe sum of 60 + 120 = 180.<\/p>\n

      Question 9.
      \n90 \u2013 45
      \nAnswer:
      \nGiven the two numbers 90 and 45
      \nWe have to find the difference of 90, 45.
      \nThe difference of 90 – 45 = 45.<\/p>\n

      Parts of a Whole<\/strong><\/p>\n

      Tell the fraction that represents the shaded part of the whole.
      \nQuestion 10.
      \n\"Envision
      \nAnswer:
      \nThe fraction that represents the shaded part of the whole number is 1\/6.<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \nThe fraction that represents the shaded part of the whole number is 1\/4.<\/p>\n

      Question 12.
      \n\"Envision
      \nAnswer:
      \nThe fraction that represents the shaded part of the whole number is 1\/10.<\/p>\n

      Dividing<\/strong><\/p>\n

      Find the quotient.
      \nQuestion 13.
      \n360 \u00f7 6
      \nAnswer:
      \nThe quotient of 360 \u00f7 6 = 60
      \n60 is the quotient.<\/p>\n

      Question 14.
      \n180 \u00f7 9
      \nAnswer:
      \nThe quotient of 180 \u00f7 9 = 20
      \n20 is the quotient.<\/p>\n

      Question 15.
      \n360 \u00f7 4
      \nAnswer:
      \nThe quotient of 360 \u00f7 4 = 90
      \n90 is the quotient.<\/p>\n

      Problem Solving<\/strong><\/p>\n

      Question 16.
      \nMake Sense and Persevere Gary has $4. Mary has twice as many dollars as Gary. Larry has 4 fewer dollars than Mary. How much money do Gary, Mary, and Larry have in all?
      \nAnswer:
      \nGiven that,
      \nTotal number of dollars at Gary = $4
      \nMary has twise as many dollars sa Gray = 2 \u00d7 $4 = $8.
      \nLarry has 4 fewer dollars than Mary = $8 – 4 = $4.
      \nTotal money with Gary, Marry, and Larry = $8 + $4 + $4 = $16.<\/p>\n

      \"Geometric<\/p>\n

      Pick a Project<\/strong><\/p>\n

      PROJECT 15A
      \nCan you find angles in stringed instruments?
      \nProject: Make a Stringed Instrument
      \n\"Envision<\/p>\n

      PROJECT 15B
      \nHow are angles important in origami?
      \nProject: Present an Origami Animal
      \n\"Envision<\/p>\n

      PROJECT 15C
      \nHow are angles formed by airplane paths?
      \nProject: Trace a Flight Plan
      \n\"Envision<\/p>\n

      3-ACT MATH PREVIEW<\/strong><\/p>\n

      Math Modeling
      \nGame of Angles
      \n\"Envision
      \nI can … model with math to solve a problem that involves measuring angles and computing with angle measures.<\/p>\n

      Lesson 15.1 Lines, Rays, and Angles<\/h3>\n

      Solve & Share<\/strong>
      \nA right angle forms a square corner, like the one shown below. Find examples of right angles in your classroom. Draw two angles that are open less than the right angle. Solve this problem any way you choose.
      \nI can … recognize and draw lines, rays, and different types of angles.
      \n\"Envision<\/p>\n

      Look Back! Reasoning Draw an angle that is open more than a right angle.<\/p>\n

      \"Geometric<\/p>\n

      Essential Question<\/strong>
      \nWhat Are Some Common Geometric Terms?<\/p>\n

      Visual Learning Bridge
      \nPoint, line, line segment, ray, right angle, acute angle, obtuse angle, and straight angle are common geometric terms.<\/p>\n

      An angle is formed by two rays that have the same endpoint.
      \n\"Envision<\/p>\n

      Convince Me! Look for Relationships Complete each figure to show the given angle.
      \n\"Envision<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhat geometric term describes a part of a line that has one endpoint? Draw an example.
      \nAnswer:
      \nA ray is a part of a line that has one endpoint and continues on forever in one direction.
      \n\"Envision<\/p>\n

      Question 2.
      \nWhat geometric term describes a part of a line that has two endpoints? Draw an example.
      \nAnswer:
      \nA line segment is a part of a line with two endpoints.
      \n\"Envision<\/p>\n

      Question 3.
      \nWhat geometric term describes an angle that forms a square corner? Draw an example.
      \nAnswer:
      \nA right angle forms a square corner.
      \n\"Envision<\/p>\n

      Do You Know How?<\/strong>
      \nFor 4-7, use geometric terms to describe what is shown.
      \nQuestion 4.
      \n\"Envision
      \nAnswer:
      \n\u2220PX represents the line segment with two end points.<\/p>\n

      Question 5.
      \n\"Envision
      \nAnswer:
      \n\u2220PQR is a right angle triangle. A right angle forms a forms a square corner.<\/p>\n

      Question 6.
      \n\"Envision
      \nAnswer:
      \n\u2220BY is a straight angle.<\/p>\n

      Question 7.
      \n\"Envision
      \nAnswer:
      \n\u2220LMN is an acute angle. An acute angle is open less than a right angle.<\/p>\n

      Independent Practice<\/strong><\/p>\n

      For 8-11, use geometric terms to describe what is shown.
      \nQuestion 8.
      \n\"Envision
      \nAnswer:
      \n\u2220HOS is an obtuse angle. An obtuse angle is open more than a right angle but less than a straight angle.<\/p>\n

      Question 9.
      \n\"Envision
      \nAnswer:
      \n\u2220BD represents the line segment with two endpoints.<\/p>\n

      \"Geometric<\/p>\n

      Question 10.
      \n\"Envision
      \nAnswer: \u2220BY is a straight angle.<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \n\u2220STP is a right angle.<\/p>\n

      For 12-15, draw the geometric figure for each term.
      \nQuestion 12.
      \nLine segment
      \nAnswer:
      \n\"Envision<\/p>\n

      Question 13.
      \nPoint
      \nAnswer:
      \n\u2022<\/p>\n

      Question 14.
      \nRay
      \nAnswer:
      \n\"Envision<\/p>\n

      Question 15.
      \nLine
      \nAnswer:
      \n\"line\"<\/p>\n

      Problem Solving<\/strong><\/p>\n

      For 16-18, use the map of Nevada. Write the geometric term that best fits each description. Draw an example.
      \n\"Envision<\/p>\n

      Question 16.
      \nBe Precise The route between 2 cities.
      \nAnswer:<\/p>\n

      Question 17.
      \nThe cities
      \nAnswer:<\/p>\n

      Question 18.
      \nThe corner formed by the north and west borders
      \nAnswer:<\/p>\n

      Question 19.
      \nVocabulary<\/strong> Write a definition for right angle. Draw a right angle. Give 3 examples of right angles in the classroom.
      \nAnswer:<\/p>\n

      Question 20.
      \nHigher Order Thinking<\/strong> Nina says she can make a right angle with an acute angle and an obtuse angle that have a common ray. Is Nina correct? Draw a picture and explain.
      \nAnswer: If an angle is acute, it can’t also be a right angle.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 21.
      \nWhich geometric term describes \u2220HJK?
      \n\"Envision
      \nA. Acute angle
      \nB. Obtuse angle
      \nC. Right angle
      \nD. Straight angle
      \nAnswer:
      \nThe geometric term \u2220HJK represents a straight angle.
      \nThus the answer is option D.<\/p>\n

      Question 22.
      \nLisa drew 2 rays that share an endpoint. Which of the following is Lisa’s drawing?
      \n\"Envision
      \nAnswer: D<\/p>\n

      Lesson 15.2 Understand Angles and Unit Angles<\/h3>\n

      Solve & Share<\/strong>
      \nIf a clock shows it is 3 o’clock, how could you describe the smaller angle made by the two hands of the clock? Solve this problem any way you choose.
      \nI can … use what I know about fractions to measure angles.
      \n\"Envision<\/p>\n

      Look Back! At 3 o’clock, what two fractions do the hands divide the clock into?<\/p>\n

      Essential Question<\/strong>
      \nWhat is the Unit Used to Measure Angles?<\/p>\n

      Visual Learning Bridge
      \nAn angle is measured with units called degrees. An angle that turns through \\(\\frac{1}{360}\\) of a circle is called a unit angle. How can you determine the angle measure of a right angle and the angles that turn through \\(\\frac{1}{6}\\) and \\(\\frac{2}{6}\\) of a circle?
      \nYou measure length in inches, area in square centimeters, and capacity in ounces. You measure an angle in degrees, o. A full circle has an
      \nangle measure of 360\u00b0.
      \n\"Envision<\/p>\n

      Divide to find the angle measure of a right angle.
      \n\"Envision
      \nRight angles divide a circle into 4 equal parts.
      \n360\u00b0 \u00f7 4 = 90\u00b0
      \nThe angle measure of a right angle is 90\u00b0.<\/p>\n

      Divide to find the measure of an angle that turns through \\(\\frac{1}{6}\\) of a circle.
      \n\"Envision
      \n\\(\\frac{1}{6}\\) of a circle is one part of the circle that is divided into 6 equal parts.
      \n360\u00b0 \u00f7 6 = 60\u00b0
      \nThe angle measure is 60\u00b0.<\/p>\n

      Add to find the measure of an angle that turns through \\(\\frac{2}{6}\\) of a circle.
      \n\"Envision
      \nRemember \\(\\frac{2}{6}\\) = \\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\)
      \nAdd to calculate the measure of \\(\\frac{2}{6}\\) of a circle.
      \n60\u00b0 + 60\u00b0 = 120\u00b0 The angle measure of of a circle is 120\u00b0.<\/p>\n

      Convince Me! Critique Reasoning Susan thinks the measure of angle B is greater than the measure of angle A. Do you agree? Explain.
      \n\"Envision<\/p>\n

      Another Example!<\/strong>
      \nFind the fraction of a circle that an angle with a measure of 45\u00b0 turns through
      \n\"Envision
      \nA 45\u00b0 angle turns through \\(\\frac{45}{360}\\) of a circle.
      \n45\u00b0 \u00d7 8 = 360\u00b0, so 45\u00b0 is \\(\\frac{1}{8}\\) of 360\u00b0.
      \nOne 45\u00b0 angle is \\(\\frac{1}{8}\\) of a circle.<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhat fraction of the circle does a 120\u00b0 angle turn through?
      \nAnswer:
      \nA circle contains 360\u00b0
      \nTo find the fraction of the circle’s 120\u00b0 angle.
      \nDivide 120\u00b0 by 360\u00b0
      \n120\u00b0\/360\u00b0 = 1\/3
      \nThus the fraction of the circle that does a 120\u00b0 angle turn through is 1\/3.<\/p>\n

      Question 2.
      \nMike cuts a pie into 4 equal pieces. What is the angle measure of each piece? Write and solve an equation.
      \nAnswer:
      \nGiven,
      \nMike cuts a pie into 4 equal pieces.
      \nA circle contains 360\u00b0
      \n360\/90 = 4
      \n90 degrees because when you cut each of them they will each measure 90 degrees.<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 3.
      \nA circle is divided into 9 equal parts. What is the angle measure of one of those parts?
      \n\"Envision
      \nAnswer:
      \nGiven that,
      \nA circle is divided into 9 equal parts.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by 9.
      \nWe have the measure for one of the nine parts of the circle, but we need two.
      \nAll we do is multiply 40 by 2 to get 80 degrees.<\/p>\n

      Question 4.
      \nAn angle turns through of the circle. What is the measure of this angle?
      \n\"Envision
      \nAnswer:
      \nAn angle turns through the circle.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by 4.
      \n360 \u00f7 4 = 90
      \nThus the measure of the angle of the above circle is 90 degrees.<\/p>\n

      Independent Practice<\/strong><\/p>\n

      For 5-8, find the measure of each angle.
      \nQuestion 5.
      \nThe angle turns through \\(\\frac{1}{5}\\) of the circle.
      \n\"Envision
      \nAnswer:
      \nAn angle turns through the circle.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by 5.
      \n360 \u00f7 5 = 72
      \nThus the measure of the angle of the above circle is 72 degrees.<\/p>\n

      Question 6.
      \nThe angle turns through \\(\\frac{3}{8}\\) of the circle.
      \n\"Envision
      \nAnswer:
      \nAn angle turns through the circle.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by \\(\\frac{3}{8}\\).
      \n360 \u00d7 \\(\\frac{3}{8}\\) = 135
      \nThus the measure of the angle of the above circle is 135 degrees.<\/p>\n

      Question 7.
      \nThe angle turns through \\(\\frac{2}{5}\\) of the circle.
      \n\"Envision
      \nAnswer:
      \nThe angle turns through \\(\\frac{2}{5}\\) of the circle.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by \\(\\frac{2}{5}\\).
      \n360 \u00d7 \\(\\frac{2}{5}\\) = 144
      \nThus the measure of the angle of the above circle is 144 degrees.<\/p>\n

      Question 8.
      \nThe angle turns through \\(\\frac{2}{6}\\) of the circle.
      \n\"Envision
      \nAnswer:
      \nThe angle turns through \\(\\frac{2}{6}\\) of the circle.
      \nThere are 360 degrees in a circle.
      \nThat means that we first divide 360 by \\(\\frac{2}{6}\\).
      \n360 \u00d7 \\(\\frac{2}{6}\\) = 120
      \nThus the measure of the angle of the above circle is 120 degrees.<\/p>\n

      Problem Solving<\/strong><\/p>\n

      Question 9.
      \nUse the clock to find the measure of the smaller angle formed by the hands at each time.
      \n\"Envision
      \na. 3:00
      \nb. 11:00
      \nc. 2:00
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-15-Geometric-Measurement-Understand-Concepts-of-Angles-and-Angle-Measurement-37\"
      \n11:00
      \nThus the correct answer is option B.<\/p>\n

      Question 10.
      \nAlgebra Jacey wrote an equation to find an angle measure. What do variables a and b represent in Jacey’s equation? 360\u00b0 \u00f7 a = b
      \nAnswer:
      \nWe know that Jacey wrote an equation to find an angle measure.
      \nThe equation is as follows:
      \n360 \u00f7 a = b
      \nSo, if the angle is 360 degrees is a central angle, i.e, an angle between 2 radii in a circle, then
      \na = the number of equal parts the circle is divided.
      \nb = the measure of the central angle of each part.<\/p>\n

      Question 11.
      \nenVision\u00ae STEM A mirror can be used to reflect a beam of light at an angle. What fraction of a circle would the angle shown turn through?
      \n\"Envision
      \nAnswer:
      \nGiven,
      \nA mirror can be used to reflect a beam of light at an angle.
      \n120\u00b0 \u00f7 360\u00b0 = 1\/3
      \nThe fraction of a circle would the angle turn is 1\/3.<\/p>\n

      Question 12.
      \nMalik paid $32.37 for three books. One book cost $16.59. The second book cost $4.27. How much did the third book cost? Use bills and coins to solve.
      \n\"Envision
      \nAnswer:
      \nGiven,
      \nMalik paid $32.37 for three books. One book cost $16.59. The second book cost $4.27.
      \n$16.59 + $4.27 = $20.86
      \n$32.37 – $20.86 = $11.51
      \nThus the cost of third book is $11.51<\/p>\n

      Question 13.
      \nMake Sense and Persevere A pie was cut into equal parts. Four pieces of the pie were eaten. The 5 pieces that remained created an angle that measured 200\u00b0. What was the angle measure of one piece of pie?
      \nAnswer:
      \nGiven that,
      \nA pie was cut into equal parts.
      \nFour pieces of the pie were eaten.
      \nThe 5 pieces that remained created an angle that measured 200\u00b0.
      \n200\/5 = 40
      \nThus the angle measure of one piece of pie is 40 degrees.<\/p>\n

      Question 14.
      \nHigher Order Thinking<\/strong> Jake cut a round gelatin dessert into 8 equal pieces. Five of the pieces were eaten. What is the angle measure of the dessert that was left?
      \nAnswer:
      \nGiven,
      \nJake cut a round gelatin dessert into 8 equal pieces.
      \nFive of the pieces were eaten.
      \nFraction is the number of pieces eaten by the total number of pieces.
      \n5\/8
      \n360 \u00d7 5\/8 = 225
      \nThus the angle measure of the desert that was left.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 15.
      \nSelect all choices that show an angle measure of 120\u00b0. Use the clock to help.
      \n\"Envision
      \n\u2610 10 o’clock
      \n\u2610 \\(\\frac{2}{6}\\) of a pie
      \n\u2610 \\(\\frac{2}{3}\\) of a circle
      \n\u2610 4 o’clock
      \n\u2610 8 o’clock
      \nAnswer: \\(\\frac{2}{6}\\) of a pie<\/p>\n

      Lesson 15.3 Measure with Unit Angles<\/h3>\n

      Solve & Share<\/strong>
      \nThe smaller angles on the tan pattern block shown each measure 30\u00b0. How can you use the angles on the pattern block to determine the measure of the angle below? Solve this problem any way you choose.
      \nI can … use angles I know to measure angles I do not know.
      \n\"Envision<\/p>\n

      Look Back! Two right angles make a straight angle. How many 45\u00b0 angles form a straight angle? Explain.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Measure Angles?<\/p>\n

      Visual Learning Bridge
      \nHolly traced around a trapezoid pattern block. She wants to find the measure of the angle formed shown to the right. What can Holly use to measure the angle?
      \n\"Envision
      \nThe measure of a unit angle is 1 degree. Just like adding inches + inches, you can add degrees + degrees. So 5\u00b0 = 1\u00b0 + 1\u00b0 + 1\u00b0 + 1\u00b0 + 1\u00b0
      \nor 5 \u00d7 1\u00b0<\/p>\n

      Use an angle you know to find the measure of another angle.
      \n\"Envision
      \nThe smaller angle of the tan pattern block measures 30\u00b0.
      \nA 30-degree angle turns through 30 one-degree angles.<\/p>\n

      The angle of the trapezoid pattern block is equal to 2 of the smaller angles of the tan pattern block. Each smaller angle is 30\u00b0.
      \n\"Envision
      \nThe measure of the trapezoid angle is 60\u00b0.
      \nA 60-degree angle turns through 60 one-degree angles.<\/p>\n

      Convince Me! Generalize What do you notice about the number of one-degree angles in an angle measure?<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nHow many 30\u00b0 angles are in a 180\u00b0 angle? Explain.
      \n\"Envision
      \nAnswer:
      \n180 \u00f7 30 = 6
      \nThus there are 6 30\u00b0 angles are in a 180\u00b0 angle.<\/p>\n

      Question 2.
      \nHow many 15\u00b0 angles are in a 180\u00b0 angle? Use your answer to Exercise 1 to explain.
      \nAnswer:
      \n180 \u00f7 15 = 12
      \nThus there are 12 15\u00b0 angles are in a 180\u00b0 angle.<\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-4, use angles you know to find the measure of each angle. Explain how the angles in the square can help.
      \nQuestion 3.
      \n\"Envision
      \nAnswer:
      \nBy seeing the above figure we can say that it is a right angle.
      \n90 \u00f7 2 = 45 degrees<\/p>\n

      Question 4.
      \n\"Envision
      \nAnswer:
      \nBy seeing the above figure we can say that it is an obtuse angle.
      \n90\u00b0 + 45\u00b0 = 135\u00b0<\/p>\n

      Independent Practice<\/strong><\/p>\n

      For 5-13, find the measure of each angle. Use pattern blocks to help.
      \nQuestion 5.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Topic-15-Geometric-Measurement-Understand-Concepts-of-Angles-and-Angle-Measurement-48\"
      \nThe measure of the angle is 70 degrees.<\/p>\n

      Question 6.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 90 degrees.<\/p>\n

      Question 7.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Topic-15-Geometric-Measurement-Understand-Concepts-of-Angles-and-Angle-Measurement-50\"
      \nThe measure of the angle is 60 degrees.<\/p>\n

      Question 8.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 110 degrees.<\/p>\n

      Question 9.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 120 degrees.<\/p>\n

      Question 10.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 90 degrees.<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 90 degrees.<\/p>\n

      Question 12.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 180 degrees.<\/p>\n

      Question 13.
      \n\"Envision
      \nAnswer:
      \nThe measure of the angle is 90 degrees.<\/p>\n

      Problem Solving<\/strong><\/p>\n

      Question 14.
      \nUse Appropriate Tools What is the measure of the angle of the yellow hexagon pattern block?
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 15.
      \nWhat is the measure of the smaller angle formed by the clock hands when it is 5:00?
      \n\"Envision
      \nAnswer: 120 degrees<\/p>\n

      Question 16.
      \nHow many 30\u00b0 angles are in a circle? Write and solve a multiplication equation to explain.
      \nAnswer:
      \nThe total angle in a circle is 360 degrees
      \n360\u00b0\/30\u00b0 = 12
      \nThus there are 120 30\u00b0 angles in a circle.<\/p>\n

      Question 17.
      \nHow many unit angles make up the smaller angle formed by the hands of a clock when it is 3:00? Explain.
      \nAnswer:
      \n3\/12 = x\u00b0\/360\u00b0
      \n1\/4 = x\u00b0\/360\u00b0
      \nx\u00b0 = 90\u00b0<\/p>\n

      Question 18.
      \nVeronica purchases a rug with a length of 16 feet and a width of 4 feet. One fourth of the rug is purple and the rest is blue. What is the area of the blue part of the rug?
      \nAnswer:
      \nVeronica purchases a rug with a length of 16 feet and a width of 4 feet.
      \nOne-fourth of the rug is purple and the rest is blue.
      \nA = base \u00d7 height
      \nArea = 16 \u00d7 4 = 64 sq. ft
      \nDetermine the blue area:
      \n64 sq. ft — 1
      \nx —- 3\/4
      \nx = 3\/4 \u00d7 64
      \nx = 192\/4
      \nx = 48 sq.ft<\/p>\n

      Question 19.
      \nHigher Order Thinking<\/strong> The hands of a clock form a 120\u00b0 angle. Name two different times it could be.
      \nAnswer:
      \nThe 120\u00b0 angles make up 1\/3 of one full rotation of the hands-on clock, with a full rotation divided up into 12 equal sections. 1\/3 of those 12 sections would be 4 sections, and since we are looking for exact hours that represent this angle, we need four sections forming each of the 120\u00b0 angles with the minute hand on the clock being at 12. Therefore, the hour hand can be at the 4 for 4 o’clock and it could also be at the 8 for 8 o’clock.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 20.
      \nThe clock reads 9:00. What is the angle measure?
      \n\"Envision
      \nA. 90\u00b0
      \nB. 180\u00b0
      \nC. 270\u00b0
      \nD. 360\u00b0
      \nAnswer:
      \nA. 90\u00b0
      \nThe angle measure is 90 degrees.
      \nThus the correct answer is option A.<\/p>\n

      Question 21.
      \nHow many 60\u00b0 angles are in 360\u00b0 angle?
      \n\"Envision
      \nA. 3
      \nB. 6
      \nC. 10
      \nD. 12
      \nAnswer: 6<\/p>\n

      Explanation:
      \n360\/60 = 6
      \nThere are 6 60\u00b0 angles are in 360\u00b0 angle.
      \nThus the correct answer is option B.<\/p>\n

      Lesson 15.4 Measure and Draw Angles<\/h3>\n

      Solve & Share<\/strong>
      \nFind the measure of ZABC. Solve this problem any way you choose.
      \nI can … use a protractor to measure and draw angles.
      \n\"Envision<\/p>\n

      Look Back! Use Appropriate Tools Use the protractor to draw an angle that measures 110\u00b0.
      \n\"Envision<\/p>\n

      Essential Question<\/strong>
      \nHow Do You Use a Protractor?<\/p>\n

      Visual Learning Bridges
      \nA protractor is a tool that is used to measure and draw angles. A partially folded crane is shown at the right. Measure \u2220PQR.
      \n\"Envision
      \nThe angle, \u2220PQR can also be written as \u2220RQP.<\/p>\n

      Measure Angles
      \nMeasure \u2220PQR.
      \nPlace the protractor’s center on the angle’s vertex, Q. Place one of the 0\u00b0 marks on \\(\\overrightarrow{Q R}\\). Read the measure where \\(\\overrightarrow{Q P}\\) crosses the protractor. If the angle is acute, use the lesser number. If the angle is obtuse, use the greater number.
      \n\"Envision
      \nThe measure of \u2220PQR is 45\u00b0.<\/p>\n

      Draw Angles
      \nDraw an angle that measures 130\u00b0.
      \nDraw \\(\\overrightarrow{T U}\\). Place the protractor so the center is over point T, and one of the 0\u00b0 marks is on \\(\\overrightarrow{T U}\\). Place a point at 130\u00b0. Label it W. Draw \\(\\overrightarrow{T W}\\).
      \n\"Envision
      \nThe measure of \u2220WTU is 130\u00b0.<\/p>\n

      Convince Me! Be Precise How do you know the measure of \u2220UTS is 60\u00b0 and not 120\u00b0?
      \n\"Envision<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhat is the angle measure of a straight line?
      \n\"Envision
      \nAnswer: The angle measure of a straight line is 0\u00b0 or 180\u00b0<\/p>\n

      Question 2.
      \nWhat are the vertex and rays of \u2220ABC? Explain.
      \nAnswer:
      \nThe vertex is the common point at which the two lines or rays are joined. Point B in the figure above is the vertex of the angle \u2220ABC.<\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-4, use a protractor to measure each angle.
      \nQuestion 3.
      \n\"Envision
      \nAnswer: 50 degrees<\/p>\n

      Question 4.
      \n\"Envision
      \nAnswer: 120 degrees<\/p>\n

      For 5-6, use a protractor to draw each angle.
      \nQuestion 5.
      \n110\u00b0
      \nAnswer:
      \n\"Angles<\/p>\n

      Question 6.
      \n50\u00b0
      \nAnswer:
      \n\"Envision<\/p>\n

      Independent Practice<\/strong><\/p>\n

      For 7-14, measure each angle. Tell if each angle is acute, right, or obtuse.
      \nRemember an acute angle is less than 90\u00b0 and an obtuse angle is greater than 90\u00b0 but less than 180\u00b0.
      \nQuestion 7.
      \n\"Envision
      \nAnswer: The above angle is greater than 90\u00b0 so it is an obtuse angle.<\/p>\n

      Question 8.
      \n\"Envision
      \nAnswer:
      \nThe above angle is less than 90\u00b0 so it is an acute angle.<\/p>\n

      Question 9.
      \n\"Envision
      \nAnswer:
      \nThe above angle is less than 90\u00b0 so it is an acute angle.<\/p>\n

      Question 10.
      \n\"Envision
      \nAnswer:
      \nThe above angle is greater than 90\u00b0 so it is an obtuse angle.<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \nThe above angle is equal to 90\u00b0 so it is a right angle.<\/p>\n

      Question 12.
      \n\"Envision
      \nAnswer:
      \nThe above angle is less than 90\u00b0 so it is an acute angle.<\/p>\n

      Question 13.
      \n\"Envision
      \nAnswer:
      \nThe above angle is greater than 90\u00b0 so it is an obtuse angle.<\/p>\n

      Question 14.
      \n\"Envision
      \nAnswer:
      \nThe above angle is less than 90\u00b0 so it is an acute angle.<\/p>\n

      For 15-18, use a protractor to draw an angle for each measure.
      \nQuestion 15.
      \n140\u00b0
      \nAnswer:
      \n\"Envision<\/p>\n

      Question 16.
      \n180\u00b0
      \nAnswer:
      \n\"Envision<\/p>\n

      Question 17.
      \n65\u00b0
      \nAnswer:
      \n\"Envision<\/p>\n

      Question 18.
      \n25\u00b0
      \nAnswer:
      \n\"Envision<\/p>\n

      Problem Solving<\/strong><\/p>\n

      Question 19.
      \nMeasure all the angles created by the intersection of Main Street and Pleasant Street. Explain how you measured.
      \n\"Envision
      \nAnswer: 25 degrees<\/p>\n

      Question 20.
      \nUse a protractor to find the measure of the angle, then use one of the angle’s rays to draw a right angle. Find the measure of the the angle that is NOT a right angle.
      \n\"Envision
      \nAnswer: 110 degrees<\/p>\n

      Question 21.
      \nCritique Reasoning<\/strong> Gail and 3 friends share half a pie. Each piece of pie is the same size. Gail believes each piece of pie has an angle measure of 25\u00b0. Is Gail correct? Explain.
      \nAnswer:
      \nGiven,
      \nGail and 3 friends share half a pie. Each piece of pie is the same size.
      \nGail believes each piece of the pie has an angle measure of 25\u00b0.
      \nHalf of a pie is 50%, divide that by three and that equals about 16.67 if you round it, but if each piece has an angle of 25, those pieces aren’t equal.<\/p>\n

      Question 22.
      \nJanet made 5 three-point shots in her first game and 3 in her second game. She also made 4 two-point shots in each game. How many total points did Janet score in the two games?
      \nAnswer: Janet score 35 points<\/p>\n

      Question 23.
      \nHigher Order Thinking<\/strong> Maya designed two intersecting roads. She drew the roads so one of the angles at the intersection was 35o. What are the three other angle measurements formed by the intersection?
      \nAnswer:
      \nTo find the other three angles in the intersection, we need to know that in an intersection of two lines, one angle is the supplement of the other, and the other two are equal to the first and the second one, that is, if the first angle is x, the values of the four angles are
      \nx, 180 – x, x and 180 – x
      \nso if one angle is 35 degrees, we have that the three other angles are 145 degrees, 35 degrees, and 145 degrees.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 24.
      \nFind the measure of the angle shown.
      \n\"Envision
      \nAnswer: 35 degrees<\/p>\n

      Question 25.
      \nFind the measure of the angle shown.
      \n\"Envision
      \nAnswer: 110 degrees<\/p>\n

      Lesson 15.5 Add and Subtract Angle Measures<\/h3>\n

      Solve & Share<\/strong>
      \nDraw \\(\\overrightarrow{B C}\\) that divides \u2220ABD into two smaller angles. Measure each angle. Solve this problem any way you choose.
      \nI can … use addition and subtraction to solve problems with unknown angle measures.
      \n\"Envision<\/p>\n

      Look Back! How can you relate the measures of the two smaller angles to the measure of the larger angle above using an equation?<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Add and Subtract to Find Unknown Angle Measures?<\/p>\n

      Visual Learning Bridge
      \nElinor designs wings for biplanes. First she draws a right angle, \u2220ABC. Then she draws \\(\\overrightarrow{B E}\\). She finds \u2220EBC measures 30\u00b0. How can Elinor find the measure of \u2220ABE without using a protractor?
      \n\"Envision
      \n\u2220ABC is decomposed into two non-overlapping parts.<\/p>\n

      \u2220EBC and \u2220ABE do not overlap, so the measure of right \u2220ABC is equal to the sum of the measures of its parts.
      \nThe measure of \u2220ABC equals the measure of \u2220ABE plus the measure of \u2220EBC.
      \n\"Envision
      \nAll right angles measure 90\u00b0<\/p>\n

      Write an equation to determine the missing angle measure.
      \nn + 30\u00b0 = 90\u00b0
      \nSolve the equation.
      \nn = 90\u00b0 \u2013 30\u00b0
      \nn = 60\u00b0
      \n\"Envision
      \nThe measure of \u2220ABE is 60\u00b0.<\/p>\n

      Convince Me! Make Sense and Persevere \u2220ABD is a straight angle. What is the measure of \u2220ABE if the measure of \u2220DBC is 115\u00b0 and the measure of \u2220CBE is 20\u00b0? How did you decide? Write and solve an equation.
      \n\"Envision<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nUse the information below to draw and label a diagram. \u2220PQR measures 45\u00b0. \u2220RQS measures 40\u00b0. \u2220PQR and \u2220RQS do not overlap. Write and solve an equation to find the measure of \u2220PQS.
      \nAnswer:
      \n\u2220PQR + \u2220RQS + n = 90<\/p>\n

      Do You Know How?<\/strong>
      \nFor 2-3, use the diagram to the right of each exercise. Write and solve an equation to find the missing angle measure.
      \nQuestion 2.
      \nWhat is the measure of \u2220EBC if \u2220ABE measures 20\u00b0?
      \n\"Envision
      \nAnswer:
      \n\u2220EBC + \u2220ABE = 90\u00b0
      \n\u2220EBC + 20\u00b0 = 90\u00b0
      \n\u2220EBC = 90\u00b0 – 20\u00b0
      \n\u2220EBC = 70\u00b0<\/p>\n

      Question 3.
      \nWhat is the measure of \u2220AEB if \u2220CEB measures 68\u00b0?
      \n\"Envision
      \nAnswer:
      \n\u2220AEB + \u2220CEB = 180\u00b0
      \n\u2220AEB + 68\u00b0 = 180\u00b0
      \n\u2220AEB = 180\u00b0 – 68\u00b0
      \n\u2220AEB = 112\u00b0<\/p>\n

      Independent Practice<\/strong><\/p>\n

      For 4-7, use the diagram to the right. Write and solve an addition or subtraction equation to find the missing angle measure.
      \n\"Envision
      \nQuestion 4.
      \nWhat is the measure of \u2220FGJ if \u2220JGH measures 22\u00b0?
      \nAnswer:
      \n\u2220FGJ + \u2220JGH = 90\u00b0
      \n\u2220FGJ + 22\u00b0 = 90\u00b0
      \n\u2220FGJ = 90\u00b0 – 22\u00b0
      \n\u2220FGJ = 68\u00b0<\/p>\n

      Question 5.
      \nWhat is the measure of \u2220KGF if \u2220EGK measures 59\u00b0?
      \nAnswer:
      \n\u2220KGF + \u2220EGK = 90\u00b0
      \n\u2220KGF + 59\u00b0= 90\u00b0
      \n\u2220KGF = 90\u00b0 – 59\u00b0
      \n\u2220KGF = 31\u00b0<\/p>\n

      Question 6.
      \nUse the angle measures you know to write an equation to find the angle measure of \u2220EGH. What kind of angle is \u2220EGH?
      \nAnswer:
      \n\u2220EGK + \u2220KGF + \u2220FGJ + \u2220JGH = 180\u00b0<\/p>\n

      Question 7.
      \nWhich two non-overlapping angles that share a ray make an obtuse angle? Use addition to explain.
      \nAnswer: \u2220KGH and \u2220EGJ are the two non-overlapping angles that share a ray that makes an obtuse angle.<\/p>\n

      Problem Solving<\/strong><\/p>\n

      Question 8.
      \nShane says a straight angle always has 180\u00b0 degrees. Is Shane correct? Explain.
      \nAnswer: Yes Shane is correct.<\/p>\n

      Question 9.
      \nModel with Math Talla earns 85\u00a2 for cans she recycles. If she gets a nickel for each can, how many cans does Talla recycle? Draw a bar diagram to represent how to solve the problem.
      \nAnswer:<\/p>\n

      Question 10.
      \nAlex draws an angle that measures 110\u00b0. He then draws a ray that divides the angle into 2 equal parts. What is the measure of each smaller angle?
      \nAnswer:
      \nTo solve for this use the expression 110\/2 since you are dividing an angle into two equal parts.
      \nWhen you simplify, you should get 55 degrees as the measure of each angle.<\/p>\n

      Question 11.
      \nSix angles share a vertex. Each of the angles has the same measure. The sum of the measures of the angles is 330\u00b0. What is the measure of one angle?
      \nAnswer:
      \nGiven,
      \nSix angles share a vertex. Each of the angles has the same measure.
      \nThe sum of the measures of the angles is 330\u00b0.
      \nThe measure of one angle is 55 because 330 divided by six is 55<\/p>\n

      Question 12.
      \nHigher Order Thinking<\/strong> Li uses pattern blocks to make a design. He puts 5 pattern blocks together, as shown in the diagram. The measure of \u2220LJK is 30\u00b0. Name all the 60\u00b0 angles shown that have point J as a vertex.
      \n\"Envision
      \nAnswer:
      \nLi uses pattern blocks to make a design.
      \nHe puts 5 pattern blocks together, as shown in the diagram.
      \nThe measure of \u2220LJK is 30\u00b0.
      \ndivide 120 by 4 you get 30 then multiply 30 by 2.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 13.
      \nCarla drew two acute non-overlapping angles that share a ray and labeled them \u2220JLK and \u2220KLM. The two angles have different measures. Carla says \u2220JLM is greater than a right angle.
      \n\"Envision
      \nPart A
      \nIs it possible for Carla to be correct? Write to explain.
      \nAnswer: No, because the acute angle is less than the right angle.<\/p>\n

      Part B
      \nWrite an equation showing one possible sum for Carla’s angles.
      \nAnswer: \u2220JLK + \u2220KLM = 90 degrees<\/p>\n

      Lesson 15.6 Problem Solving<\/h3>\n

      Use Appropriate Tools<\/strong>
      \nSolve & Share<\/strong>
      \nCaleb is standing next to the tallest building in a city. Determine the measure of the 3 angles with the vertex at the tallest building and rays on the music hall, the live theater, and the art museum. Tell what tool you used and explain why the measures make sense relative to each other.
      \nI can … use appropriate tools strategically to solve problems.
      \n\"Envision<\/p>\n

      Thinking Habits
      \nBe a good thinker! These questions can help you.<\/p>\n

        \n
      • Which tools can I use?<\/li>\n
      • Why should I use this tool to help me solve the problem?<\/li>\n
      • Is there a different tool I could use?<\/li>\n
      • Am I using the tool appropriately?<\/li>\n<\/ul>\n

        Look Back! Use Appropriate Tools Could you use a ruler to find the angle measures? Explain.<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Select and Use Appropriate Tools to Solve Problems?<\/p>\n

        Visual Learning Bridge
        \nTrevor and Holly are drawing trapezoids to make a design. They need to find the measures of the angles formed by the sides of the trapezoid and the length of each side of the trapezoid. What tools are needed to find the measures of the angles and the lengths of the sides?
        \n\"Envision
        \nWhat do you need to do to copy the trapezoid?
        \nI need to measure the angles, then measure the sides.<\/p>\n

        Which tool can I use to help me solve this problem?
        \nI can<\/p>\n

          \n
        • decide which tool is appropriate.<\/li>\n
        • explain why it is the best tool to use.<\/li>\n
        • use the tool correctly.<\/li>\n<\/ul>\n

          Here’s my thinking.
          \nUse a protractor to measure the angles. The angles measure 120\u00b0 and 60\u00b0.
          \n\"Envision
          \nThen, use a ruler to measure the length of each side. The lengths are \\(\\frac{3}{4}\\) inch, \\(\\frac{3}{4}\\) inch, \\(\\frac{3}{4}\\) inch, and 1\\(\\frac{1}{2}\\) inches.
          \n\"Envision<\/p>\n

          Convince Me! Use Appropriate Tools What other tools could be used to solve this problem? Why are a protractor and a ruler more appropriate than other tools?<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Lee brought 1\\(\\frac{3}{5}\\) pounds of apples to the picnic. Hannah brought \\(\\frac{4}{5}\\) pound of oranges. Lee said they brought 2\\(\\frac{2}{5}\\) pounds of fruit in all. Lee needs to justify that 1\\(\\frac{3}{5}\\) + \\(\\frac{4}{5}\\) = 2\\(\\frac{2}{5}\\)
          \n\"Envision
          \nQuestion 1.
          \nWhat tool could Lee use to justify the sum?
          \nAnswer: Fraction strips<\/p>\n

          Question 2.
          \nHow can Lee use a tool to justify the sum? Draw pictures of the tool you used to explain.
          \nAnswer:<\/p>\n

          Independent Practice<\/strong><\/p>\n

          Use Appropriate Tools<\/strong>
          \nWhat are the measures of the sides and angles of the parallelogram shown? Use Exercises 3-5 to help solve.
          \n\"Envision
          \nQuestion 3.
          \nWhat tools can you use to solve this problem?
          \nAnswer:<\/p>\n

          Question 4.
          \nExplain how to use the tool you chose to find the measures of the angles. Label the figure with the measures you find.
          \nAnswer:<\/p>\n

          Question 5.
          \nExplain how to use the tool you chose to find the lengths of the sides. Label the figure with the measures you find.
          \nAnswer:<\/p>\n

          Problem Solving<\/strong><\/p>\n

          Performance Task<\/strong><\/p>\n

          Mural
          \nBefore Nadia paints a mural, she plans what she is going to paint. She sketches the diagram shown and wants to know the measures of \u2220WVX, \u2220WVY, \u2220XWY, and \u2220YVZ.
          \n\"Envision<\/p>\n

          Question 6.
          \nReasoning<\/strong> What quantities are given in the problem and what do the numbers mean? What do you know from the diagram?
          \nAnswer:<\/p>\n

          Question 7.
          \nMake Sense and Persevere What do you need to find?
          \nAnswer:<\/p>\n

          Question 8.
          \nUse Appropriate Tools Measure \u2220WVX, \u2220WVY, and \u2220YVZ. What is the best tool to use?
          \n\"Envision
          \nAnswer:<\/p>\n

          Question 9.
          \nModel with Math Write and solve an equation which could be used to find the measure of \u2220XVY. What is the measure of the angle?
          \nAnswer:<\/p>\n

          Topic 15 Fluency Practice Activity<\/h3>\n

          Follow the path<\/strong>
          \nShade a path from START to FINISH. Follow sums and differences that are between 20,000 and 25,000. You can only move up, down, right, or left.
          \nI can … add and subtract multi-digit whole numbers.
          \n\"Envision<\/p>\n

          Answer:
          \n\"Envision-Math-Common-Core-Grade-4-Answer-Key-Topic-15-Geometric-Measurement-Understand-Concepts-of-Angles-and-Angle-Measurement-100\"<\/p>\n

          Topic 15 Vocabulary Review<\/h3>\n

          Word List<\/p>\n

            \n
          • acute angle<\/li>\n
          • angle measure<\/li>\n
          • degree (0)<\/li>\n
          • line<\/li>\n
          • line segment<\/li>\n
          • obtuse angle<\/li>\n
          • point<\/li>\n
          • protractor<\/li>\n
          • ray<\/li>\n
          • right angle<\/li>\n
          • straight angle<\/li>\n
          • unit angle<\/li>\n
          • vertex<\/li>\n<\/ul>\n

            Understand Vocabulary<\/p>\n

            Question 1.
            \nCross out the terms that do NOT describe an angle with a square corner.
            \nacute angle
            \nright angle
            \nobtuse angle
            \nstraight angle
            \nAnswer: Straight angle.<\/p>\n

            Explanation:
            \nWe can describe acute angle, obtuse angle, right angle with a square corner. A straight angle cannot be described with a square corner.
            \nThus the answer is option D.<\/p>\n

            Question 2.
            \nCross out the terms that do NOT describe an angle open less than a right angle.
            \nacute angle
            \nright angle
            \nobtuse angle
            \nstraight angle
            \nAnswer:
            \nobtuse angle, straight angle are the terms that do NOT describe an angle open less than a right angle.<\/p>\n

            Question 3.
            \nCross out the terms that do NOT describe an angle that forms a straight line.
            \nacute angle
            \nright angle
            \nobtuse angle
            \nstraight angle
            \nAnswer:
            \nacute angle, right angle, obtuse angle are the terms that do NOT describe an angle that forms a straight line.<\/p>\n

            Question 4.
            \nCross out the terms that do NOT describe an angle open more than a right angle, but less than a straight angle.
            \nacute angle
            \nright angle
            \nobtuse angle
            \nstraight angle
            \nAnswer:
            \nacute angle, right angle and straight angle are the terms that do NOT describe an angle open more than a right angle, but less than a straight angle.<\/p>\n

            Label each example with a term from the Word List.
            \nQuestion 5.
            \n\"Envision ___________
            \nAnswer: straight line, because it has does not have endpoints.<\/p>\n

            Question 6.
            \n\"Envision ___________
            \nAnswer: ray, because it has one endpoint.<\/p>\n

            Question 7.
            \n\"Envision ___________
            \nAnswer: line segment, because it has two endpoints.<\/p>\n

            Question 8.
            \n\"Envision ____________
            \nAnswer: 2 rays with a single endpoint<\/p>\n

            Use Vocabulary in Writing<\/strong>
            \nQuestion 9.
            \nDescribe how to measure an angle. Use at least 3 terms from the Word List in your explanation.
            \nAnswer: We can measure an angle using a protractor, compass, and blocks.<\/p>\n

            Topic 15 Reteaching<\/h3>\n

            Set A pages 549-552<\/strong><\/p>\n

            A ray has one endpoint and continues on forever in one direction.
            \nA line segment is a part of a line with two endpoints.
            \nAn angle is formed by two rays with a common endpoint.
            \n\"Envision<\/p>\n

            Remember<\/strong> that a line segment is a part of a line.<\/p>\n

            Use geometric terms to describe what is shown.
            \nQuestion 1.
            \n\"Envision
            \nAnswer: line segment, because it has two endpoints.<\/p>\n

            Question 2.
            \n\"Envision
            \nAnswer: right angle<\/p>\n

            Question 3.
            \n\"Envision
            \nAnswer: obtuse angle<\/p>\n

            Question 4.
            \n\"Envision
            \nAnswer: ray, because it has one endpoint<\/p>\n

            Set B pages 553-556<\/strong><\/p>\n

            The angle below is \\(\\frac{1}{3}\\) of the circle.
            \n\"Envision
            \n\\(\\frac{1}{3}\\) means 1 of 3 equal parts.
            \n360\u00b0 \u00f7 3 = 120\u00b0
            \nThe measure of this angle is 120\u00b0.<\/p>\n

            Remember<\/strong> there are 360\u00b0 in a circle.<\/p>\n

            A circle is cut into eighths. What is the angle measure of each piece?
            \n\"Envision
            \nQuestion 1.
            \nUse division to solve.
            \nAnswer:
            \nGiven,
            \nA circle is cut into eighths.
            \n360\/8 = 45 degrees
            \n90\/2 = 45 degrees<\/p>\n

            Question 2.
            \nUse multiplication to solve.
            \nAnswer:<\/p>\n

            Set C pages 557-560<\/strong><\/p>\n

            You can use an angle you know to find the measure of other angles. The smaller angle of the tan pattern block has a measure of 30\u00b0
            \n\"Envision
            \nThree of the 30\u00b0 angles will fit into the angle.
            \nAdd: 30\u00b0 + 30\u00b0 + 30o = 90\u00b0
            \nThe measure of this angle is 90\u00b0.<\/p>\n

            Remember<\/strong> you can use any angle that you know the measure of to find the measure of other angles.<\/p>\n

            Find the measure of each angle. Use pattern blocks.
            \nQuestion 1.
            \n\"Envision
            \nAnswer: 55 degrees<\/p>\n

            Question 2.
            \n\"Envision
            \nAnswer: 110 degrees<\/p>\n

            Set D pages 561-564<\/strong><\/p>\n

            \"Envision
            \nThe measure of this angle is 60\u00b0.<\/p>\n

            Remember<\/strong> that a straight angle has a measure of 180\u00b0.<\/p>\n

            Measure the angles.
            \nQuestion 1.
            \n\"Envision
            \nAnswer: 90 degrees<\/p>\n

            Question 2.
            \n\"Envision
            \nAnswer: 120 degrees<\/p>\n

            Set E pages 565-568<\/strong><\/p>\n

            When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.
            \n\"Envision<\/p>\n

            Remember<\/strong> you can subtract to find angle measures.<\/p>\n

            \u2220ABD is decomposed into two non-overlapping angles, \u2220ABC and \u2220CBD. Complete the table.
            \n\"Envision
            \nAnswer:<\/p>\n

            Set F pages 569-572<\/strong><\/p>\n

            Think about these questions to help you use appropriate tools strategically.
            \nThinking Habits<\/p>\n

              \n
            • Which tools can I use?<\/li>\n
            • Why should I use this tool to help me solve the problem?<\/li>\n
            • Is there a different tool could use?<\/li>\n
            • Am I using the tool appropriately?
              \n\"Envision<\/li>\n<\/ul>\n

              Remember<\/strong> there may be more than one appropriate tool to use to solve a problem.<\/p>\n

              One-eighth of the pie is missing from the tin.
              \nQuestion 1.
              \nWhat tools can Delia use to measure the angle of the missing piece?
              \nAnswer: protractor can be used to measure the angle of the missing piece.<\/p>\n

              Question 2.
              \nHow can you calculate the measure?
              \nAnswer: We can calculate the measure of an angle using protractor.<\/p>\n

              Topic 15 Assessment Practice<\/h3>\n

              Question 1.
              \nWhat is the measure of the angle shown below? Name a type of angle that has an angle measure greater than the angle shown.
              \n\"Envision
              \nAnswer:
              \nThe measure of the angle is 35 degrees.
              \nThe name of the angle is an acute angle.<\/p>\n

              Question 2.
              \nMegan needs to find the measures of the angles on a bridge.
              \n\"Envision
              \nA. Find the measure of \u2220YXW if \u2220YXZ is 85\u00b0 and \u2220ZXW is 40\u00b0. Write and solve an addition equation.
              \nAnswer:<\/p>\n

              B. Find the measure of \u2220CAD if \u2220CAB is a right angle and \u2220DAB is 45\u00b0. Write and solve a subtraction equation.
              \nAnswer:<\/p>\n

              Question 3.
              \nIf you divide a circle into 360 equal angles, what is the angle measure of each angle?
              \nAnswer:
              \nyou divide a circle into 360 equal angles
              \n360 \u00f7 6 = 60 degree
              \n60 + 60 + 60 + 60 + 60 + 60
              \nThus the angle measure of each angle is 60 degrees.<\/p>\n

              Question 4.
              \nChoose the correct term from the box to complete each statement.
              \nLine Segment
              \nRay
              \nA __________ has one endpoint.
              \nA __________ has two endpoints.
              \nAnswer:
              \nA Ray has one endpoint.
              \nA Line segment has two endpoints.<\/p>\n

              Question 5.
              \nDraw an example of a line \\(\\overleftrightarrow{R S}\\). Label a point T between points Rand S. Using point T, draw ray \\(\\overrightarrow{T V}\\).
              \nAnswer:<\/p>\n

              Question 6.
              \nJKL is a straight angle decomposed into 2 non-overlapping angles, \u2220JKM and \u2220MKL. If \u2220MKL measures 104\u00b0, what type of angle is \u2220JKM? What is the measure of \u2220JKM?
              \nAnswer:<\/p>\n

              Question 7.
              \n\u2220ABC has a measure of 40\u00b0and \u2220CBD has a measure of 23\u00b0. The angles share a ray and form ZABD. Write and solve an equation to find the measure of \u2220ABD.
              \nAnswer: \u2220ABC + \u2220CBD + \u2220ABD = 90\u00b0<\/p>\n

              Question 8.
              \nEmma cuts slices from pies. Match each fraction with the equal angle measure.
              \n\"Envision
              \nAnswer:
              \n\"Envision-Math-Common-Core-Grade-4-Answers-Topic-15-Geometric-Measurement-Understand-Concepts-of-Angles-and-Angle-Measurement-123\"<\/p>\n

              Question 9.
              \nSelect all the true statements.
              \n\u2610 An acute angle is open less than a right angle.
              \n\u2610 An obtuse angle makes a square corner.
              \n\u2610 A right angle is open less than an obtuse angle.
              \n\u2610 A straight angle forms a straight line.
              \n\u2610 All obtuse angles have the same measure.
              \nAnswer:
              \n\u2610 An acute angle is open less than a right angle.
              \n\u2610 A right angle is open less than an obtuse angle.
              \n\u2610 A straight angle forms a straight line.
              \nThus A, C, D are the true statements.<\/p>\n

              Question 10.
              \nTwo wooden roof beams meet at a 60\u00b0 angle. Draw an angle to represent how the beams meet.
              \nAnswer:<\/p>\n

              Question 11.
              \nWhich geometric term best describes the light that shines from a flashlight?
              \n\"Envision
              \nA. Point
              \nB. Ray
              \nC. Line segment
              \nD. Line
              \nAnswer: Ray<\/p>\n

              Question 12.
              \nTerry is measuring \u2220RST using pattern blocks. The smaller angle of each of the tan pattern blocks shown below measures 30\u00b0. What is the measure of \u2220RST? Explain.
              \n\"Envision
              \nAnswer:
              \nGiven,
              \nTerry is measuring \u2220RST using pattern blocks.
              \nThe smaller angle of each of the tan pattern blocks shown below measures 30\u00b0.
              \nThus the measure of \u2220RST is 30\u00b0 + 30\u00b0 + 30\u00b0 + 30\u00b0 = 120<\/p>\n

              Question 13.
              \nIdentify an acute angle, a right angle, and an obtuse angle in the figure below.
              \n\"Envision
              \nAnswer:
              \n\u2220AEB is an acute angle
              \n\u2220DEC is a right angle
              \n\u2220BED is an obtuse angle<\/p>\n

              Topic 15 Performance Task<\/h3>\n

              Ancient Roads
              \nThe ancient Romans built roads throughout their empire. Many roads were paved with stones that fit together. The spaces between the stones were filled with sand and gravel. Many of these roads still exist today, over 2,000 years after they were built.<\/p>\n

              Question 1.
              \nAs seen in the Roman Road figure, the stones formed angles and geometric figures.
              \n\"Envision<\/p>\n

              Part A
              \nWhat geometric figure has one endpoint at F and goes on forever through point G?
              \nAnswer: E<\/p>\n

              Part B
              \nIs \u2220EDA right, acute, or obtuse? Explain.
              \nAnswer:
              \n\u2220EDA is an obtuse angle.<\/p>\n

              Part C
              \n\u2220EDG turns through \\(\\frac{1}{8}\\) of a circle. What is its angle measure? Explain.
              \nAnswer:
              \n\u2220EDG turns through \\(\\frac{1}{8}\\) of a circle.
              \n80<\/p>\n

              Question 2.
              \nAnswer the following to find the measure of \u2220HJK and \u2220HJL in the Measuring a Roman Road figure.
              \n\"Envision
              \nPart A
              \nName two tools you could use to measure the angles.
              \nAnswer: Protractor and blocks pattern could be used to measure the angles.<\/p>\n

              Part B
              \nThe smaller angle of the tan pattern block measures 30\u00b0, as shown in the Tan Pattern Block figure. A 30-degree angle is 30 one-degree angles. What is the measure of \u2220HJK in the Measuring a Roman Road figure? Explain.
              \n\"Envision
              \nAnswer:<\/p>\n

              Part C
              \nWhat is the measure of \u2220HJL in the Measuring a Roman Road figure? Write and solve an equation to find the measure of the angle.
              \nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"

              Go through the\u00a0enVision Math Common Core Grade 4 Answer Key\u00a0Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 4th Grade Answers Key Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement Essential Questions: What are some common geometric terms? How …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/10689"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=10689"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/10689\/revisions"}],"predecessor-version":[{"id":27789,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/10689\/revisions\/27789"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=10689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=10689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=10689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}