Question

what is the measure of $overline{xy}$?

Explanation:

Step1: Recall circle - arc relationship

The sum of the measures of arcs in a circle is 360°.

Step2: Identify known arcs

We know that the arc $\overset{\frown}{ZV}$ has a measure of 43° and the angles at the center related to the other arcs form right - angles. The arc $\overset{\frown}{ZY}$ is a semi - circle (since the angle at the center is 180°).

Step3: Calculate $\overset{\frown}{XY}$

The measure of arc $\overset{\frown}{XY}=360^{\circ}- 90^{\circ}-90^{\circ}-43^{\circ}=137^{\circ}$.

Answer:

D. 137°