Explanation Definitions used: Vertical angles: When two lines intersect, four angles are formed. Two angles that are opposite to each other are called vertical angles. Vertical angles have the same measure. Adjacent angles: Two angles that share a common side are called adjacent angles. Adjacent angles formed by intersecting lines are supplementary. That is, the sum of their measures is 180 ° . Calculation: The measures of the angles ∠ x , ∠ y , and ∠ z , can be obtained as follows. From the given figure, it can be noticed that ∠ y and the angle of measure 62 ° are vertical angles. Thus, by the property of vertical angles, ∠ y and the angle of measure 62 ° have same measures. Thus, m ∠ y = 62 ° . Since ∠ x and the angle of measure 62 ° are adjacent angles, sum of their measures equals to 180 ° . Thus, the value of m ∠ x can be obtained as follows. m ∠ x + 62 ° = 180 ° m ∠ x = 180 ° − 62 ° m ∠ x = 118 ° Then measure of angle ∠ x equals 118 °

Basic College Mathematics, Books A La Carte Edition, Plus Mylab Math With Pearson Etext -- Access Card Package (6th Edition)

6th Edition

ISBN: 9780134844978

Author: Elayn Martin-Gay

Publisher: PEARSON

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Chapter 8, Problem 4T

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The measures of the angles ∠x, ∠y, and ∠z from the given figure.

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Chapter 8 Solutions

Basic College Mathematics, Books A La Carte Edition, Plus Mylab Math With Pearson Etext -- Access Card Package (6th Edition)

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Classify each angle as acute, right, obtuse, or...Ch. 8.1 - Find the complement of a 29° angle. Ch. 8.1 - Find the supplement of a 67° angle. Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 1VRV Ch. 8.1 - Prob. 2VRV

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The measures of the angles ∠ x , ∠ y , and ∠ z from the given figure.

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Chapter 8 Solutions