Question

angle mon is a straight angle and $overrightarrow{op}$ bisects $angle moq$. what is the measure of $angle mop$?$\bigcirc$ $29^circLXB0\bigcirc$ $61^circ$$\bigcirc$ $122^circ$

Explanation:

Step1: Find ∠MOQ

Since ∠MON is a straight angle ($180^\circ$), and ∠QON = $58^\circ$, calculate ∠MOQ:
$\angle MOQ = 180^\circ - 58^\circ = 122^\circ$

Step2: Bisect ∠MOQ to get ∠MOP

$\overrightarrow{OP}$ bisects ∠MOQ, so divide ∠MOQ by 2:
$\angle MOP = \frac{122^\circ}{2} = 61^\circ$

Answer:

61° (Option C)