Question

Find m 86 W X • N 156 Y

Answer 1

Given:

A circle with center Z and the points W, X, Y are on the circumference of the circle.

To find:

The measure of angle WXY.

Solution:

From the given figure, we get

$Arc(XY)=156^\circ$

$Arc(WX)=86^\circ$

The measure of arc of the complete circle is 360 degrees.

$Arc(WX)+Arc(XY)+Arc(WY)=360^\circ$

$86^\circ+156^\circ+Arc(WY)=360^\circ$

$Arc(WY)=360^\circ-86^\circ-156^\circ$

$Arc(WY)=118^\circ$

The measure of arc WY is 118 degrees. It means the central angle on this arc is also 118 degrees.

$m\angle WZY=118^\circ$

According to the central angle theorem, the inscribed angle on an arc is always half of its central angle.

$m\angle WXY=\dfrac{m\angle WZY}{2}$

$m\angle WXY=\dfrac{118^\circ}{2}$

$m\angle WXY=59^\circ$

Therefore, the correct option is A.