In the given figure, O is the center of the circle. If arc MK = 143° and arc KL = 77°, find the measure of ∠MKL.

Insight:

Step-by-step solution:

1. Step 1: Identify the intercepted arc for the angle ∠MKL. The inscribed angle ∠MKL intercepts arc ML.
2. Step 2: Calculate the measure of arc ML. The sum of arcs in a circle is 360°. So, arc ML = 360° - arc MK - arc KL = 360° - 143° - 77° = 360° - 220° = 140°.
3. Step 3: Apply the inscribed angle theorem. The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, $$m∠MKL = \frac{1}{2} imes m( ext{arc } ML)$$.
4. Step 4: Calculate the measure of ∠MKL. $$m∠MKL = \frac{1}{2} imes 140° = 70°$$.

Answer: 70°