Question

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

Explanation:

Step1: Find the measure of ∠MOQ

Since ∠MON is a straight angle ($180^{\circ}$) and ∠QON = $58^{\circ}$, then ∠MOQ=∠MON - ∠QON.
$$\angle MOQ=180^{\circ}- 58^{\circ}=122^{\circ}$$

Step2: Use the angle - bisector property

Because $\overrightarrow{OP}$ bisects ∠MOQ, by the definition of an angle bisector (an angle bisector divides an angle into two equal parts), if ∠MOQ = $122^{\circ}$, then ∠MOP=$\frac{1}{2}\angle MOQ$.
$$\angle MOP=\frac{122^{\circ}}{2}=61^{\circ}$$

Answer:

61°