Question

what is the measure of ∠xyz? 33° 75° a. 54° b. 75° c. 108° d. 33°

Explanation:

Step1: Recall the 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. The measure of arc XZ is \(75^{\circ}\).

Step3: Calculate the measure of ∠XYZ

By the inscribed - angle theorem, \(m\angle XYZ=\frac{1}{2}\text{ measure of arc }XZ\). Since the measure of arc XZ is \(75^{\circ}\), then \(m\angle XYZ = 75^{\circ}\).

Answer:

B. \(75^{\circ}\)