Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-5 Proportions in Triangles - Practice and Problem-Solving Exercises - Page 478: 52


$m \angle X = 52^{\circ}$

Work Step by Step

In two similar triangles, corresponding angles are congruent. Let's list the congruent angles: $\angle V ≅ \angle P$ $\angle L ≅ \angle S$ $\angle Q ≅ \angle X$ We can now use the triangle sum theorem to find the measure of the third angle, $\angle Q$ of $\triangle VLQ$: $m \angle Q = 180 - (m \angle V + m \angle L)$ Substitute in what we are given: $m \angle Q = 180 - (48 + 80)$ Evaluate what's in parentheses first: $m \angle Q = 180 - (128)$ Subtract to solve: $m \angle Q = 52^{\circ}$ If $\angle Q ≅ \angle X$, then $m \angle Q = m \angle X$; therefore, $m \angle X = 52^{\circ}$.
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