Question

In the diagram, $\overleftrightarrow{\mathit{O}\mathit{T}}$bisects $\angle SOU$, $m\angle UOV=35$, and $m\angle YOW=120$. Find the measure of each angle.

$m\angle VOW$

Short answer

The measure of the angle $\angle VOW$ is $25°$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the relations between the angles YOW, VOW and UOV.

From the diagram it can be noticed that:

The angles $YOW,VOW$and $UOV$lies on a straight line $YU$.

Therefore, sum of the angles $YOW,VOW$and $UOW$is $180°$.

Therefore,$\angle YOW+\angle VOW+\angle UOV=180°$

Step 3. Find the measure of the angle VOW.

As, $\angle YOW+\angle VOW+\angle UOV=180°$.

Therefore,

$$\begin{gathered} \angle YOW+\angle VOW+\angle UOV=180° \\ 120°+\angle VOW+35°=180° \\ 155°+\angle VOW=180° \\ \angle VOW=180°-155° \\ \angle VOW=25° \end{gathered}$$

Therefore, the measure of the angle $VOW$is$25°$