{"id":79572,"date":"2022-06-09T09:16:28","date_gmt":"2022-06-09T03:46:28","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=79572"},"modified":"2022-05-10T14:18:32","modified_gmt":"2022-05-10T08:48:32","slug":"eureka-math-grade-7-module-3-lesson-11","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-3-lesson-11\/","title":{"rendered":"Eureka Math Grade 7 Module 3 Lesson 11 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 11 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 3 Lesson 11 Example Answer Key<\/h3>\n

Example 1.
\nThe following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angles 86\u00b0, 68\u00b0, and the angle between them, which is vertically opposite and equal in measure to x, are angles on a line and have a sum of 180\u00b0.
\n86 + x + 68 = 180
\nx + 154 = 180
\nx + 154 – 154 = 180 – 154
\nx = 26<\/p>\n

Example 2.
\nIn a complete sentence, describe the angle relationships in the diagram. You may label the diagram to help describe the angle relationships. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angle formed by adjacent angles a\u00b0 and b\u00b0 is vertically opposite to the 77\u00b0 angle. The angles x\u00b0, a\u00b0, and b\u00b0 are adjacent angles that have a sum of 90\u00b0 (since the adjacent angle is a right angle and together the angles are on a line).
\nx + 77 = 90
\nx + 77 – 77 = 90 – 77
\nx = 13<\/p>\n

Example 3.
\nIn a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Find the measures of \u2220JAH and \u2220GAF. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe sum of the degree measurements of \u2220JAH, \u2220GAH, \u2220GAF, and the arc that subtends \u2220JAF is 360\u00b0.
\n225 + 2x + 90 + 3x = 360
\n315 + 5x = 360
\n315 – 315 + 5x = 360 – 315
\n5x = 45
\n(\\(\\frac{1}{5}\\))5x = (\\(\\frac{1}{5}\\))45
\nx = 9
\nm\u2220JAH = 2(9\u00b0) = 18\u00b0 m\u2220GAF = 3(9\u00b0) = 27\u00b0<\/p>\n

Example 4.
\nIn the accompanying diagram, the measure of \u2220DBE is four times the measure of \u2220FBG.
\n\"Engage
\na. Label \u2220DBE as y\u00b0 and \u2220FBG as x\u00b0. Write an equation that describes the relationship between \u2220DBE and \u2220FBG.
\nAnswer:
\ny = 4x<\/p>\n

b. Find the value of x.
\nAnswer:
\n50 + x + 4x = 180
\n50 + 5x = 180
\n5x + 50 – 50 = 180 – 50
\n5x = 130
\n(\\(\\frac{1}{5}\\))(5x) = (\\(\\frac{1}{5}\\))(130)
\nx = 26<\/p>\n

c. Find the measures of \u2220FBG, \u2220CBD, \u2220ABF, \u2220GBE, and \u2220DBE.
\nAnswer:
\nm\u2220FBG = 26\u00b0
\nm\u2220CBD = 26\u00b0
\nm\u2220ABF = 4(26\u00b0) = 104\u00b0
\nm\u2220GBE = 50\u00b0
\nm\u2220DBE = 104\u00b0<\/p>\n

d. What is the measure of \u2220ABG? Identify the angle relationship used to get your answer.
\nAnswer:
\n\u2220ABG = \u2220ABF + \u2220FBG
\n\u2220ABG = 104 + 26
\n\u2220ABG = 130
\nm\u2220ABG = 130\u00b0
\nTo determine the measure of \u2220ABG, you need to add the measures of adjacent angles \u2220ABF and \u2220FBG.<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 11 Exercise Answer Key<\/h3>\n

Opening Exercise
\na. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angles marked by x\u00b0, 90\u00b0, and 14\u00b0 are angles on a line and have a sum of 180\u00b0.
\nx + 90 + 14 = 180
\nx + 104 = 180
\nx + 104 – 104 = 180 – 104
\nx = 76<\/p>\n

b. \\(\\overleftrightarrow{C D}\\) and \\(\\overleftrightarrow{E F}\\) are intersecting lines. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for y. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe adjacent angles marked by y\u00b0 and 51\u00b0 together form the angle that is vertically opposite and equal to the angle measuring 147\u00b0.
\ny + 51 = 147
\ny + 51 – 51 = 147 – 51
\ny = 96<\/p>\n

c. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for b. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe adjacent angles marked by 59\u00b0, 41\u00b0, b\u00b0, 65\u00b0, and 90\u00b0 are angles at a point and together have a sum of 360\u00b0.
\n59 + 41 + b + 65 + 90 = 360
\nb + 255 = 360 – 255
\nb = 105<\/p>\n

d. The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for z. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angles marked by z\u00b0, 158\u00b0, and z\u00b0 are angles on a line and have a sum of 180\u00b0.
\nz + 158 + z = 180
\n2z + 158 = 180
\n2z + 158 – 158 = 180 – 158
\n2z = 22
\nz = 11<\/p>\n

e. Write an equation for the angle relationship shown in the figure and solve for x. In a complete sentence, describe the angle relationship in the diagram. Find the measurements of \u2220EPB and \u2220CPA. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\n\u2220CPA, \u2220CPE, and \u2220EPB are angles on a line and their measures have a sum of 180\u00b0.
\n5x + 90 + x = 180
\n6x + 90 = 180
\n6x + 90 – 90 = 180 – 90
\n6x = 90
\n(\\(\\frac{1}{6}\\))6x = (\\(\\frac{1}{6}\\))90
\nx = 15
\n\u2220EPB = 15\u00b0
\n\u2220CPA = 5(15\u00b0) = 75\u00b0<\/p>\n

Exercise 1.
\nThe following figure shows four lines intersecting at a point. In a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angles x\u00b0, 25\u00b0, y\u00b0, and 40\u00b0 are angles on a line and have a sum of 180\u00b0; the angle marked y\u00b0 is vertically opposite and equal to 96\u00b0.
\ny = 96, vert. \u2220s
\nx + 25 + (96) + 40 = 180
\nx + 161 = 180
\nx + 161 – 161 = 180 – 161
\nx = 19<\/p>\n

Exercise 2.
\nIn a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y. Confirm your answers by measuring the angles with a protractor.
\n\"Engage
\nAnswer:
\nThe measures of angles x and y have a sum of 90\u00b0; the measures of angles x and 27 have a sum of 90\u00b0.
\nx + 27 = 90
\nx + 27 – 27 = 90 – 27
\nx = 63
\n(63) + y = 90
\n63 – 63 + y = 90 – 63
\ny = 27<\/p>\n

Exercise 3.
\nIn a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Find the measure of \u2220JKG. Confirm your answer by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe sum of the degree measurements of \u2220LKJ, \u2220JKG, \u2220GKM, and the arc that subtends \u2220LKM is 360\u00b0.
\n5x + 24 + x + 90 = 360
\n6x + 114 = 360
\n6x + 114 – 114 = 360 – 114
\n6x = 246
\n(\\(\\frac{1}{6}\\))6x = (\\(\\frac{1}{6}\\))246
\nx = 41
\nm\u2220JKG = 41\u00b0<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 11 Problem Set Answer Key<\/h3>\n

In a complete sentence, describe the angle relationships in each diagram. Write an equation for the angle relationship(s) shown in the figure, and solve for the indicated unknown angle. You can check your answers by measuring each angle with a protractor.
\nQuestion 1.
\nFind the measures of \u2220EAF, \u2220DAE, and \u2220CAD.
\n\"Eureka
\nAnswer:
\n\u2220GAF, \u2220EAF, \u2220DAE, and \u2220CAD are angles on a line and their measures have a sum of 180\u00b0.
\n6x + 4x + 2x + 30 = 180
\n12x + 30 = 180
\n12x + 30 – 30 = 180 – 30
\n12x = 150
\nx = 12.5
\nm\u2220EAF = 2(12.5\u00b0) = 25\u00b0
\nm\u2220DAE = 4(12.5\u00b0) = 50\u00b0
\nm\u2220CAD = 6(12.5\u00b0) = 75\u00b0<\/p>\n

Question 2.
\nFind the measure of a.
\n\"Eureka
\nAnswer:
\nAngles a\u00b0, 26\u00b0, a\u00b0, and 126\u00b0 are angles at a point and have a sum of 360\u00b0.
\na + 126 + a + 26 = 360
\n2a + 152 = 360
\n2a + 152 – 152 = 360 – 152
\n2a = 208
\n(\\(\\frac{1}{2}\\))2a = (\\(\\frac{1}{2}\\))208
\na = 104<\/p>\n

Question 3.
\nFind the measures of x and y.
\n\"Eureka
\nAnswer:
\nAngles y\u00b0 and 65\u00b0 and angles 25\u00b0 and x\u00b0 have a sum of 90\u00b0.
\nx + 25 = 90
\nx + 25 – 25 = 90 – 25
\nx = 65
\n65 + y = 90
\n65 + y = 90
\n65 – 65 + y = 90 – 65
\ny = 25<\/p>\n

Question 4.
\nFind the measure of \u2220HAJ.
\n\"Eureka
\nAnswer:
\nAdjacent angles x\u00b0 and 15\u00b0 together are vertically opposite from and are equal to angle 81\u00b0.
\nx + 15 = 81
\nx + 15 – 15 = 81 – 15
\nx = 66
\nm\u2220HAJ = 66\u00b0<\/p>\n

Question 5.
\nFind the measures of \u2220HAB and \u2220CAB.
\n\"Eureka
\nAnswer:
\nThe measures of adjacent angles \u2220CAB and \u2220HAB have a sum of the measure of \u2220CAH, which is vertically opposite from and equal to the measurement of \u2220DAE.
\n2x + 3x + 70 = 180
\n5x = 110
\n(\\(\\frac{1}{5}\\))5x = (\\(\\frac{1}{5}\\))110
\nx = 22
\nm\u2220HAB = 3(22\u00b0) = 66\u00b0
\nm\u2220CAB = 2(22\u00b0) = 44\u00b0<\/p>\n

Question 6.
\nThe measure of \u2220SPT is b\u00b0. The measure of \u2220TPR is five more than two times \u2220SPT. The measure of \u2220QPS is twelve less than eight times the measure of \u2220SPT. Find the measures of \u2220SPT, \u2220TPR, and \u2220QPS.
\n\"Eureka
\nAnswer:
\n\u2220QPS, \u2220SPT, and \u2220TPR are angles on a line and their measures have a sum of 180\u00b0.
\n(8b – 12) + b + (2b + 5) = 180
\n11b – 7 = 180
\n11b – 7 + 7 = 180 + 7
\n11b = 187
\n(\\(\\frac{1}{11}\\))11b = (\\(\\frac{1}{11}\\))187
\nb = 17
\nm\u2220SPT = (17\u00b0) = 17\u00b0
\nm\u2220TPR = 2(17\u00b0) + 5\u00b0 = 39\u00b0
\nm\u2220QPS = 8(17\u00b0) – 12\u00b0 = 124\u00b0<\/p>\n

Question 7.
\nFind the measures of \u2220HQE and \u2220AQG.
\n\"Eureka
\nAnswer:
\n\u2220AQG, \u2220AQH, and \u2220HQE are adjacent angles whose measures have a sum of 90\u00b0.
\n2y + 21 + y = 90
\n3y + 21 = 90
\n3y + 21 – 21 = 90 – 21
\n3y = 69
\n(\\(\\frac{1}{3}\\))3y = (\\(\\frac{1}{3}\\))69
\ny = 23
\nm\u2220HQE = 2(23\u00b0) = 46\u00b0
\nm\u2220AQG = (23\u00b0) = 23\u00b0<\/p>\n

Question 8.
\nThe measures of three angles at a point are in the ratio of 2:3:5. Find the measures of the angles.
\nAnswer:
\n\u2220A = 2x, \u2220B = 3x, \u2220C = 5x
\n2x + 3x + 5x = 360
\n10x = 360
\n(\\(\\frac{1}{10}\\))10x = (\\(\\frac{1}{10}\\))360
\nx = 36
\n\u2220A = 2(36\u00b0) = 72\u00b0
\n\u2220B = 3(36\u00b0) = 108\u00b0
\n\u2220C = 5(36\u00b0) = 180\u00b0<\/p>\n

Question 9.
\nThe sum of the measures of two adjacent angles is 72\u00b0. The ratio of the smaller angle to the larger angle is 1\u22363. Find the measures of each angle.
\nAnswer:
\n\u2220A = x, \u2220B = 3x
\nx + 3x = 72
\n4x = 72
\n(\\(\\frac{1}{4}\\))(4x) = (\\(\\frac{1}{4}\\))(72)
\nx = 18
\n\u2220A = (18\u00b0) = 18\u00b0
\n\u2220B = 3(18\u00b0) = 54\u00b0<\/p>\n

Question 10.
\nFind the measures of \u2220CQA and \u2220EQB.
\n\"Eureka
\nAnswer:
\n4x + 5x = 108
\n9x = 108
\n(\\(\\frac{1}{9}\\))9x = (\\(\\frac{1}{9}\\))108
\nx = 12
\nm\u2220CQA = 5(12\u00b0) = 60\u00b0
\nm\u2220EQB = 4(12\u00b0) = 48\u00b0<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 11 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nWrite an equation for the angle relationship shown in the figure and solve for x. Find the measures of \u2220RQS and \u2220TQU.
\n\"Eureka
\nAnswer:
\n3x + 90 + 4x + 221 = 360
\n7x + 311 = 360
\n7x + 311 – 311 = 360 – 311
\n7x = 49
\n(\\(\\frac{1}{7}\\))7x = (\\(\\frac{1}{7}\\))49
\nx = 7
\nm\u2220RQS = 3(7\u00b0) = 21\u00b0
\nm\u2220TQU = 4(7\u00b0) = 28\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 11 Answer Key Eureka Math Grade 7 Module 3 Lesson 11 Example Answer Key Example 1. The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in … 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\/79572"}],"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=79572"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79572\/revisions"}],"predecessor-version":[{"id":137620,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79572\/revisions\/137620"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}