Question

what is the measure of ∠xyz? a. 72° b. 36° c. 17° d. 55°

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 of ∠XYZ

The intercepted arc of ∠XYZ is arc XZ, and the measure of arc XZ is 17°.

Step3: Calculate the measure of ∠XYZ

By the inscribed - angle theorem, the measure of ∠XYZ is half of the measure of arc XZ. So, m∠XYZ=\frac{1}{2}\times17° = 17°.

Answer:

C. 17°