Question

in the diagram of circle o, what is the measure of ∠boc? 27°, 54°, 108°, 120°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The inscribed angle ∠BAC intercepts arc BC. Given that the central angle corresponding to arc BC is 108°.

Step3: Calculate the measure of ∠BAC

By the inscribed - angle theorem, m∠BAC=$\frac{1}{2}$m(arc BC). Since m(arc BC) = 108°, then m∠BAC=$\frac{108^{\circ}}{2}$ = 54°.

Answer:

54°