If angle $\angle MON$ is a straight angle and bisects angle $\angle MOQ$, what is the measure of angle $\angle MOP$?

• A. $58°$
• B. $122°$
• C. $29°$
• D. $61°$

Answer: (A)

Verified step by step guidance

1. Understand that angle \( \angle MON \) is a straight angle, which means its measure is \( 180^\circ \).
2. Recognize that \( \angle MON \) bisects \( \angle MOQ \), meaning \( \angle MON \) divides \( \angle MOQ \) into two equal parts.
3. Express the relationship: if \( \angle MON \) bisects \( \angle MOQ \), then \( \angle MON = \frac{1}{2} \times \angle MOQ \).
4. Since \( \angle MON = 180^\circ \), set up the equation \( 180^\circ = \frac{1}{2} \times \angle MOQ \) and solve for \( \angle MOQ \).
5. Use the value of \( \angle MOQ \) to find \( \angle MOP \) by subtracting the known angles or using the given relationships in the figure.