In the given figure, O is the center of the circle. If arc MN = 46° and arc NK = 112°, find the measure of ∠MKN.

Insight:

Step-by-step solution:

1. Step 1: Identify the intercepted arc for the angle ∠MKN. The inscribed angle ∠MKN intercepts arc MN.
2. Step 2: The measure of arc MN is given as 46°.
3. Step 3: Apply the inscribed angle theorem: $$m∠MKN = \frac{1}{2} imes m( ext{arc } MN)$$.
4. Step 4: Calculate the measure of ∠MKN. $$m∠MKN = \frac{1}{2} imes 46° = 23°$$.

Answer: 23°