Chapter 2.4, Problem 15WE

To determine

To calculate:Themeasure of $m\angle VOW$

Answer to Problem 15WE

The measure of $m\angle VOW$ is ${25}^{\circ }$

Explanation of Solution

Given information:

  

  $\overrightarrow{OT}$ bisects $\angle SOU,m\angle UOV=35,$ and $m\angle YOW=120.$

Since the angles $\angle SOY$ and $\angle YOW$ forms a linear pair.

Therefore, $\angle YOW={120}^{\circ }$

Thus,

  $\begin{array}{cc}SOY+\angle YOW={180}^{\circ }& \\ \angle SOY+{120}^{\circ }={180}^{\circ }& \\ \angle SOY={180}^{\circ }-{120}^{\circ }& \\ \angle SOY={60}^{\circ }& \end{array}$

As $\angle SOY$ and $\angle UOW$ are vertically opposite angles and therefore are equal

  $\angle SOY={60}^{\circ }$

Thus, $\angle UOW={60}^{\circ }$

Also, from the figure, $m\angle UOV={35}^{\circ }$

From Angle addition postulate,

  $\begin{array}{l}m\angle UOW=m\angle UOV+m\angle VOW\\ {60}^{\circ }={35}^{\circ }+m\angle VOW\\ m\angle VOW={25}^{\circ }\end{array}$

Thus, the measure of the angle $m\angle VOW$ is ${25}^{\circ }$