Explanation Given: The given statement is, D C ¯ ∥ A B ¯ ∠ A ≅ ∠ C m ∠ A = 3 x + y m ∠ D = 5 x + 10 And, m ∠ C = 5 y + 20 Figure ( 1 ) Property: ( 1 ) If two parallel lines are cut by transversal, then a pair of corresponding interior angles on the same side of a transversal is supplementary. ( 2 ) Supplementary angles add up to 180 ° . Calculation: The given statement is, D C ¯ ∥ A B ¯ ∠ A ≅ ∠ C m ∠ A = 3 x + y m ∠ D = 5 x + 10 And, m ∠ C = 5 y + 20 ∠ A and ∠ B are congruent angles. So, m ∠ A = m ∠ C . Substitute 3 x + y for m ∠ A and 5 y + 20 for m ∠ C in the above equation. 3 x + y = 5 y + 20 3 x + y − 5 y = 20 3 x − 4 y = 20 ⋯ ( 1 ) ∠ A and ∠ D are corresponding interior angles on the same side of a transversal. So, m ∠ A + m ∠ D = 180 Substitute 3 x + y for m ∠ A and 5 x + 10 for m ∠ D in the above equation

Elementary Geometry for College Students

6th Edition

ISBN: 9781285195698

Author: Daniel C. Alexander, Geralyn M. Koeberlein

Publisher: Cengage Learning

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Chapter 2.CR, Problem 18CR

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The measure of ∠B.

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Chapter 2 Solutions

Elementary Geometry for College Students

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To find: The measure of ∠B.

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Chapter 2 Solutions

To find:

The measure of ∠B.