angle mon is a straight angle and $overrightarrow{op}$ bisects $angle moq$. what is the measure of $angle…

Explanation:

Step1: Recall the measure of a straight - angle

A straight - angle MON has a measure of 180°. So, $\angle MOQ+\angle QON = 180^{\circ}$. Given $\angle QON = 58^{\circ}$, then $\angle MOQ=180^{\circ}-\angle QON$. $\angle MOQ = 180 - 58=122^{\circ}$

Step2: Use the angle - bisector property

Since $\overrightarrow{OP}$ bisects $\angle MOQ$, by the definition of an angle - bisector, $\angle MOP=\frac{1}{2}\angle MOQ$. $\angle MOP=\frac{1}{2}\times122^{\circ}=61^{\circ}$

Answer:

$61^{\circ}$