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 - Page 125: 19



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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.