Question

question 2 of 10 what is the measure of $widehat{xy}$ shown in the diagram below?

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

The inscribed angle $\angle XZY$ intercepts arc $\overset{\frown}{XY}$. The measure of the other arc $\overset{\frown}{VW}=110^{\circ}$. The sum of the measures of the two arcs of the circle is $360^{\circ}$. Let the measure of arc $\overset{\frown}{XY}=x$. Then $x + 110^{\circ}=360^{\circ}$, so $x=360^{\circ}- 110^{\circ}=250^{\circ}$.

Step3: Calculate the measure of the inscribed angle

The measure of inscribed angle $\angle XZY=\frac{1}{2}\text{ (measure of arc }\overset{\frown}{XY})$. Since the measure of arc $\overset{\frown}{XY} = 71^{\circ}$, then $\angle XZY=\frac{71^{\circ}}{2}=35.5^{\circ}$.

Answer:

D. 35.5°