\nEstimate the measurement of x. ___
\nIn a complete sentence, describe the angle relationship in the diagram.
\n
![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Example-Answer-Key-1.png\")
\nAnswer:
\n\u2220BAC and \u2220CAD are angles on a line and their measures have a sum of 180\u00b0.<\/p>\n
Example 1.
\nEstimate the measurement of x. ___
\nIn a complete sentence, describe the angle relationship in the diagram.
\n
\nAnswer:
\n\u2220BAC and \u2220CAD are angles on a line and their measures have a sum of 180\u00b0.<\/p>\n
Write an equation for the angle relationship shown in the figure and solve for x. Then, find the measures of \u2220BAC and confirm your answers by measuring the angle with a protractor.
\nx + 132 = 180
\nx + 132 – 132 = 180 – 132
\nx = 48
\nm\u2220BAC = 48\u00b0<\/p>\n
Example 2.
\nIn a complete sentence, describe the angle relationship in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Example-Answer-Key-3.png\")
\nAnswer:
\n\u2220AEL and \u2220LEB are angles on a line and their measures have a sum of 180\u00b0. \u2220AEL and \u2220KEB are vertical angles and are of equal measurement.<\/p>\n
Write an equation for the angle relationship shown in the figure and solve for x and y. Find the measurements of \u2220LEB and \u2220KEB.
\nAnswer:
\ny = 144\u00b0; m\u2220KEB = 144\u00b0 (or vert. \u2220s are = )
\nx + 144 = 180
\nx + 144 – 144 = 180 – 144
\nx = 36
\nm\u2220LEB = 36\u00b0<\/p>\n
Example 3.
\nIn a complete sentence, describe the angle relationships in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Example-Answer-Key-5.png\")
\nAnswer:
\n\u2220GKE, \u2220EKF, and \u2220GKF are angles at a point and their measures have a sum of 360\u00b0.<\/p>\n
Write an equation for the angle relationship shown in the figure and solve for x. Find the measurement of \u2220EKF and confirm your answers by measuring the angle with a protractor.
\nAnswer:
\nx + 90 + 135 = 360
\nx + 225 = 360
\nx + 225 – 225 = 360 – 225
\nx = 135
\nm\u2220EKF = 135\u00b0<\/p>\n
Example 4.
\nThe following two lines intersect. The ratio of the measurements of the obtuse angle to the acute angle in any adjacent angle pair in this figure is 2:1. In a complete sentence, describe the angle relationships in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Example-Answer-Key-7.png\")
\nAnswer:
\nThe measurement of an obtuse angle is twice the measurement of an acute angle in the diagram.<\/p>\n
Label the diagram with expressions that describe this relationship. Write an equation that models the angle relationship and solve for x. Find the measurements of the acute and obtuse angles.
\nAnswer:
\n2x + 1x = 180
\n3x = 180
\n(\\(\\frac{1}{3}\\))(3x) = (\\(\\frac{1}{3}\\))(180)
\nx = 60
\nAcute angle = 60\u00b0
\nObtuse angle = 2x\u00b0 = 2(60\u00b0) = 120\u00b0<\/p>\n
Use the diagram to complete the chart.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Opening-Exercise-Answer-Key-50.png\")
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Opening-Exercise-Answer-Key-51.png\")
<\/p>\n
Exercise 1.
\nIn a complete sentence, describe the angle relationship in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Exercise-Answer-Key-2.png\")
\nAnswer:
\n\u2220BAC, \u2220CAD, and \u2220DAE are angles on a line and their measures have a sum of 180\u00b0.<\/p>\n
Find the measurements of \u2220BAC and \u2220DAE.
\nAnswer:
\n3x + 90 + 2x = 180
\n5x + 90 = 180
\n5x + 90 – 90 = 180 – 90
\n(\\(\\frac{1}{5}\\))(5x) = (\\(\\frac{1}{5}\\))(90)
\nx = 18
\nm\u2220BAC = 3(18\u00b0) = 54\u00b0
\nm\u2220DAE = 2(18\u00b0) = 36\u00b0<\/p>\n
Exercise 2.
\nIn a complete sentence, describe the angle relationships in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Exercise-Answer-Key-4.png\")
\nAnswer:
\n\u2220JEN and \u2220NEM are adjacent angles and, when added together, are the measure of \u2220JEM; \u2220JEM and \u2220KEL are vertical angles and are of equal measurement.<\/p>\n
Write an equation for the angle relationship shown in the figure and solve for x.
\nAnswer:
\n3x + 16 = 85
\n3x + 16 – 16 = 85 – 16
\n3x = 69
\n(\\(\\frac{1}{3}\\))3x = 69(\\(\\frac{1}{3}\\))
\nx = 23<\/p>\n
Exercise 3.
\nIn a complete sentence, describe the angle relationships in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Exercise-Answer-Key-6.png\")
\nAnswer:
\n\u2220EAH, \u2220GAH, \u2220GAF, and \u2220FAE are angles at a point and their measures sum to 360\u00b0.<\/p>\n
Find the measurement of \u2220GAH.
\nAnswer:
\n(x + 1) + 59 + 103 + 167 = 360
\nx + 1 + 59 + 103 + 167 = 360
\nx = 30
\nm\u2220GAH = (30 + 1)\u00b0 = 31\u00b0<\/p>\n
Exercise 4.
\nThe ratio of m\u2220GFH to m\u2220EFH is 2\u22363. In a complete sentence, describe the angle relationships in the diagram.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Exercise-Answer-Key-8.png\")
\nAnswer:
\nThe measurement of \u2220GFH is \\(\\frac{2}{3}\\) the measurement of \u2220EFH; The measurements of \u2220GFH and \u2220EFH have a sum of 90\u00b0.<\/p>\n
Find the measures of \u2220GFH and \u2220EFH.
\nAnswer:
\n2x + 3x = 90
\n5x = 90
\n(\\(\\frac{1}{5}\\))(5x) = (\\(\\frac{1}{5}\\))(90)
\nx = 18
\nm\u2220GFH = 2(18\u00b0) = 36\u00b0
\nm\u2220EFH = 3(18\u00b0) = 54\u00b0<\/p>\n
For each question, use angle relationships to write an equation in order to solve for each variable. Determine the indicated angles. You can check your answers by measuring each angle with a protractor.<\/p>\n
Question 1.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurement of \u2220DAE.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-3.1.png\")
\nAnswer:
\nOne possible response: \u2220CAD, \u2220DAE, and \u2220FAE are angles on a line and their measures sum to 180\u00b0.
\n90 + x + 65 = 180
\nx + 155 = 180
\nx + 155 – 155 = 180 – 155
\nx = 25
\nm\u2220DAE = 25\u00b0<\/p>\n
Question 2.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurement of \u2220QPR.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-15.png\")
\nAnswer:
\n\u2220QPR, \u2220RPS, and \u2220SPT are angles on a line and their measures sum to 180\u00b0.
\nf + 154 + f = 180
\n2f + 154 = 180
\n2f + 154 – 154 = 180 – 154
\n2f = 26
\n(\\(\\frac{1}{2}\\))2f = (\\(\\frac{1}{2}\\))26
\nf = 13
\nm\u2220QPR = 13\u00b0<\/p>\n
Question 3.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurements of \u2220CQD and \u2220EQF.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-16.png\")
\nAnswer:
\n\u2220BQC, \u2220CQD, \u2220DQE, \u2220EQF, and \u2220FQG are angles on a line and their measures sum to 180\u00b0.
\n10 + 2x + 103 + 3x + 12 = 180
\n5x + 125 = 180
\n5x + 125 – 125 = 180 – 125
\n5x = 55
\n(\\(\\frac{1}{5}\\))5x = (\\(\\frac{1}{5}\\))55
\nx = 11
\nm\u2220CQD = 2(11\u00b0) = 22\u00b0
\nm\u2220EQF = 3(11\u00b0) = 33\u00b0<\/p>\n
Question 4.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measure of x.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-20.png\")
\nAnswer:
\nAll of the angles in the diagram are angles at a point and their measures sum to 360\u00b0.
\n4(x + 71) = 360
\n4x + 284 = 360
\n4x + 284 – 284 = 360 – 284
\n4x = 76
\n(\\(\\frac{1}{4}\\))4x = (\\(\\frac{1}{4}\\))76
\nx = 19<\/p>\n
Question 5.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures of x and y.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-21.png\")
\nAnswer:
\n\u2220CKE, \u2220EKD, and \u2220DKB are angles on a line and their measures sum to 180\u00b0. Since \u2220FKA and \u2220AKE form a straight angle and the measurement of \u2220FKA is 90\u00b0, \u2220AKE is 90\u00b0, making \u2220CKE and \u2220AKC form a right angle and their measures have a sum of 90\u00b0.
\nx + 25 + 90 = 180
\nx + 115 = 180
\nx + 115 – 115 = 180 – 115
\nx = 65<\/p>\n
(65) + y = 90
\n65 – 65 + y = 90 – 65
\ny = 25<\/p>\n
Question 6.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures of x and y.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-22.png\")
\nAnswer:
\n\u2220EAG and \u2220FAK are vertical angles and are of equal measurement. \u2220EAG and \u2220GAD form a right angle and their measures have a sum of 90\u00b0.
\n2x + 24 = 90
\n2x + 24 – 24 = 90 – 24
\n2x = 66
\n(\\(\\frac{1}{2}\\))2x = (\\(\\frac{1}{2}\\))66
\nx = 33
\n3y = 66
\n(\\(\\frac{1}{3}\\))3y = (\\(\\frac{1}{3}\\))66
\ny = 22<\/p>\n
Question 7.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures of \u2220CAD and \u2220DAE.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-25.png\")
\nAnswer:
\n\u2220CAD and \u2220DAE form a right angle and their measures have a sum of 90\u00b0.
\n(\\(\\frac{3}{2}\\) x + 20) + 2x = 90
\n\\(\\frac{7}{2}\\) x + 20 = 90
\n\\(\\frac{7}{2}\\) x + 20 – 20 = 90 – 20
\n\\(\\frac{7}{2}\\) x = 70
\n(\\(\\frac{2}{7}\\)) \\(\\frac{7}{2}\\) x = 70(\\(\\frac{2}{7}\\))
\nx = 20
\nm\u2220CAD = \\(\\frac{3}{2}\\) (20\u00b0) + 20\u00b0 = 50\u00b0
\nm\u2220DAE = 2(20\u00b0) = 40\u00b0<\/p>\n
Question 8.
\nIn a complete sentence, describe the relevant angle relationships in the following diagram. Find the measure of \u2220CQG.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-18.1.png\")
\nAnswer:
\n\u2220DQE and \u2220CQF are vertical angles and are of equal measurement. \u2220CQG and \u2220GQF are adjacent angles and their measures sum to the measure of \u2220CQF.
\n3x + 56 = 155
\n3x + 56 – 56 = 155 – 56
\n3x = 99
\n(\\(\\frac{1}{3}\\))3x = (\\(\\frac{1}{3}\\))99
\nx = 33
\nm\u2220CQG = 3(33\u00b0) = 99\u00b0<\/p>\n
Question 9.
\nThe ratio of the measures of a pair of adjacent angles on a line is 4:5.
\na. Find the measures of the two angles.
\nAnswer:
\n\u22201 = 4x, \u22202 = 5x
\n4x + 5x = 180
\n9x = 180
\n(\\(\\frac{1}{9}\\))9x = (\\(\\frac{1}{9}\\))180
\nx = 20
\n\u22201 = 4(20\u00b0) = 80\u00b0
\n\u22202 = 5(20\u00b0) = 100\u00b0<\/p>\n
b. Draw a diagram to scale of these adjacent angles. Indicate the measurements of each angle.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-30.png\")
<\/p>\n
Question 10.
\nThe ratio of the measures of three adjacent angles on a line is 3:4:5.
\na. Find the measures of the three angles.
\nAnswer:
\n\u22201 = 3x, \u22202 = 4x, \u22203 = 5x
\n3x + 4x + 5x = 180
\n12x = 180
\n(\\(\\frac{1}{12}\\))12x = (\\(\\frac{1}{12}\\))180
\nx = 15
\n\u22201 = 3(15\u00b0) = 45\u00b0
\n\u22202 = 4(15\u00b0) = 60\u00b0
\n\u22203 = 5(15\u00b0) = 75\u00b0<\/p>\n
b. Draw a diagram to scale of these adjacent angles. Indicate the measurements of each angle.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-10-Problem-Set-Answer-Key-30.1.png\")
<\/p>\n
In a complete sentence, describe the relevant angle relationships in the following diagram. That is, describe the angle relationships you could use to determine the value of x.
\nAnswer:
\n\u2220KAE and \u2220EAF are adjacent angles whose measurements are equal to \u2220KAF; \u2220KAF and \u2220JAG are vertical angles and are of equal measurement.<\/p>\n
Use the angle relationships described above to write an equation to solve for x. Then, determine the measurements of \u2220JAH and \u2220HAG.
\n![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-7th-Grade-Module-3-Lesson-10-Exit-Ticket-Answer-Key-20.png\")
\nAnswer:
\n5x + 3x = 90 + 30
\n8x = 120
\n(\\(\\frac{1}{8}\\))(8x) = (\\(\\frac{1}{8}\\))(120)
\nx = 15
\nm\u2220JAH = 3(15\u00b0) = 45\u00b0
\nm\u2220HAG = 5(15\u00b0) = 75\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"
Engage NY Eureka Math 7th Grade Module 3 Lesson 10 Answer Key Eureka Math Grade 7 Module 3 Lesson 10 Example Answer Key Example 1. Estimate the measurement of x. ___ In a complete sentence, describe the angle relationship in the diagram. Answer: \u2220BAC and \u2220CAD are angles on a line and their measures have … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79516"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=79516"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79516\/revisions"}],"predecessor-version":[{"id":137638,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79516\/revisions\/137638"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}