Question

question 8 of 10 what is the measure of (widehat{xz})?

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, the inscribed angle is \(36^{\circ}\) and the arc \(\widehat{yz}\) is the intercepted arc.

Step2: Calculate the measure of arc \(\widehat{yz}\)

Let the measure of arc \(\widehat{yz}\) be \(m\). According to the inscribed - angle theorem, if the inscribed angle \(\angle xyz = 36^{\circ}\), then \(m = 2\times\angle xyz\). So \(m=2\times36^{\circ}=72^{\circ}\).

Answer:

A. \(72^{\circ}\)