Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-6 Proving Angles Congruent - Practice and Problem-Solving Exercises: 19

Answer

50

Work Step by Step

Let the angle whose measure is labeled as $x^o$ be $\angle X$. Let the angle whose measure is labeled as $y^o$ be $\angle Y$. The unlabeled angle is complementary to $\angle Y$. Call this angle $\angle U$. The problem and diagram tell us that $m\angle U$ is 40, since the angles adjacent to the perpendicular line are the same. $m\angle U+m\angle Y=90\longrightarrow$ definition of complementary angles $40+m\angle Y=90\longrightarrow$ substitute the given value for $m\angle U$ $m\angle Y=50$ Theorem 2.3 tells that angles that are complementary to congruent angles are also congruent, so $m\angle X$ is also 50.
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