In the given figure, O is the center of the circle. If arc NQ = 200°, find the measure of ∠NMQ.

Insight:

Step-by-step solution:

1. Step 1: Identify the intercepted arc for the angle ∠NMQ. The inscribed angle ∠NMQ intercepts arc NKQ.
2. Step 2: Calculate the measure of arc NKQ. The entire circle is 360°. The arc NQ is given as 200°. Therefore, the remaining arc NKQ = 360° - 200° = 160°.
3. Step 3: Apply the inscribed angle theorem. The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, $$m∠NMQ = \frac{1}{2} imes m( ext{arc } NKQ)$$.
4. Step 4: Calculate the measure of ∠NMQ. $$m∠NMQ = \frac{1}{2} imes 160° = 80°$$.

Answer: 80°