Question

question 9 of 10
what is the measure of $overparen{xy}$?
a. 133°
b. 43°
c. 137°
d. 47°

Explanation:

Step1: Recall circle - angle relationship

The sum of angles around a point is 360°.

Step2: Identify known angles

We know two 90 - degree angles and a 43 - degree angle at the center of the circle. Let the measure of arc \(XY\) be \(m\). The central angle corresponding to arc \(XY\) is \(m\) (the measure of an arc is equal to the measure of its central angle).

Step3: Set up equation

\(90 + 90+43 + m=360\).

Step4: Solve for \(m\)

First, add the known angles: \(90 + 90+43=223\). Then, \(m = 360 - 223=137\) for the major - arc \(XY\). But we want the minor - arc \(XY\). The sum of the major and minor arcs of a circle is 360°. So the measure of minor - arc \(XY\) is \(360 - 137 - 90 - 90 - 43=47^{\circ}\).

Answer:

D. 47°