Answer the given questions about the indicated examples of this section.

In Example 1, if ∠AOB = 72° in Fig. 2.78, then what is the measure of ∠OAB?

Data from Example 1

In Fig. 2.78, O is the center of the circle, and AB is tangent at B. If ∠OAB = 25°, find ∠AOB.

Because the center is O, OB is a radius of the circle. A tangent is perpendicular to a radius at the point of tangency, which means ∠ABO = 90° so that ∠OAB + ∠OBA = 25° + 90° = 115°

Because the sum of the angles of a triangle is 180°, we have ∠AOB = 180° − 115° = 65°

B Fig. 2.78 0