Question

what is the measure of (widehat{xy})? 42° 42° 38° a. 40° b. 42° c. 46° d. 38°

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Angles $\angle XZY$ and $\angle UZV$ are vertical angles. Given $\angle UZV = 42^{\circ}$, so $\angle XZY=42^{\circ}$.

Step2: Recall the measure of an arc

The measure of an arc is equal to the measure of the central angle that subtends it. The central angle for arc $\widehat{XY}$ is $\angle XZY$.

Answer:

B. $42^{\circ}$