Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - Chapter Review - Page 343: 18


$\angle PXY = 45^{\circ}$

Work Step by Step

If $P$ is the incenter, that means this is the point where all angle bisectors meet. Because $\angle YXZ$ is bisected by $\overline{PX}$, $m \angle PXY$ is congruent to $m \angle PXZ$ and would be half of $m \angle YXZ$, which is $90^{\circ}$. Both angles, $\angle PXY$ and $\angle PXZ$, have a measure of $45^{\circ}$.
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