Question

What is the measure of MOP?

Answer 1

Answer:

(C) ${\angle}MOP=61^{\circ}$

Step-by-step explanation:

Given: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

To find: The measure of the angle MOP.

Solution: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

Thus, using the straight line property, we get

${\angle}MOP+{\angle}POQ+{\angle}QON=180^{\circ}$

$2{\angle}MOP+{\angle}QON=180^{\circ}$

Substituting the given values, we get

$2{\angle}MOP+58^{\circ}=180^{\circ}$

$2{\angle}MOP=122^{\circ}$

${\angle}MOP=61^{\circ}$

Hence, option (C) is correct.