Explanation From the given figure, the measure of an angle m ∡ A B C = 125 ° . The measure of an angle m ∡ A B C form a supplementary with an angle m ∡ D B E . Hence, m ∡ A B C + m ∡ D B E = 180 ° 125 ° + m ∡ D B E = 180 ° ( ∵ m ∡ A B C = 125 ° ) m ∡ D B E = 180 ° − 125 ° m ∡ D B E = 55 ° The line segment D E ¯ is transversal to the parallel lines l 1 and l 2 . Then, by the definition of alternate interior angle m ∡ E D F = 55 ° . In triangle Δ E D F the measure of an angle m ∡ D F E is obtained as follows, m ∡ D E F + m ∡ E D F + m ∡ D F E = 180 °

A Survey of Mathematics with Applications (10th Edition) - Standalone book

10th Edition

ISBN: 9780134112107

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 8.2, Problem 76E

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The measure of the angle m∡DEC from the given figure.

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Chapter 8.2, Problem 75E

Chapter 8.2, Problem 77E

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The measure of the angle m ∡ D E C from the given figure.

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