In the given figure, O is the center of the circle. If m∠AOB = 60°, find the measure of ∠APB.

Insight:

Step-by-step solution:

1. Step 1: Identify the arc subtending the angles. Arc AB subtends ∠AOB at the center and ∠APB at the circumference.
2. Step 2: Apply the theorem relating the central angle and the inscribed angle subtended by the same arc. The theorem states that the angle at the center is twice the angle at the circumference. Therefore, $$m∠AOB = 2 imes m∠APB$$.
3. Step 3: Substitute the given value of ∠AOB and solve for ∠APB. Given $$m∠AOB = 60°$$. So, $$60° = 2 imes m∠APB$$.
4. Step 4: Calculate the measure of ∠APB. $$m∠APB = 60° / 2 = 30°$$.

Answer: 30°