## Basic College Mathematics (10th Edition)

Published by Pearson

# Chapter 8 - Geometry - 8.2 Angles and Their Relationships - 8.2 Exercises - Page 543: 20

#### Answer

$\angle$ROS = 105$^{\circ}$ $\angle$POQ = 35$^{\circ}$ $\angle$ROQ = 40$^{\circ}$ $\angle$TOS = 35$^{\circ}$

#### Work Step by Step

$\angle$POU and $\angle$ROS are vertical angles. This means that they are equal. Therefore $\angle$ROS = 105$^{\circ}$ $\angle$UOT and $\angle$ROQ are vertical angles. This means that they are equal. Therefore $\angle$ROQ = 40$^{\circ}$ The sum of $\angle$POU, $\angle$POQ, and $\angle$UOT equals 180$^{\circ}$. This is due to $\angle$QOT being a Straight Angle. $\angle$POQ = 180$^{\circ}$ - (105$^{\circ}$ + 40$^{\circ}$) $\angle$POQ = 180$^{\circ}$ - 145$^{\circ}$ $\angle$POQ = 35$^{\circ}$ $\angle$POQ and $\angle$ROQ are vertical angles. This means that they are equal. Therefore $\angle$ROQ = 40$^{\circ}$

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