Question

angle mon is a straight angle and op bisects ∠moq. what is the measure of ∠mop? 29° 61° 122° 58°

Explanation:

Step1: Recall straight - angle property

A straight angle $\angle MON = 180^{\circ}$. Given $\angle NOQ=58^{\circ}$, we find $\angle MOQ$.
$\angle MOQ=180^{\circ}-\angle NOQ = 180 - 58=122^{\circ}$

Step2: Use angle - bisector property

Since $OP$ bisects $\angle MOQ$, then $\angle MOP=\frac{1}{2}\angle MOQ$.
$\angle MOP=\frac{1}{2}\times122^{\circ}=61^{\circ}$

Answer:

$61^{\circ}$