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
[tex]Arc(XY)=156^\circ[/tex]
[tex]Arc(WX)=86^\circ[/tex]
The measure of arc of the complete circle is 360 degrees.
[tex]Arc(WX)+Arc(XY)+Arc(WY)=360^\circ[/tex]
[tex]86^\circ+156^\circ+Arc(WY)=360^\circ[/tex]
[tex]Arc(WY)=360^\circ-86^\circ-156^\circ[/tex]
[tex]Arc(WY)=118^\circ[/tex]
The measure of arc WY is 118 degrees. It means the central angle on this arc is also 118 degrees.
[tex]m\angle WZY=118^\circ[/tex]
According to the central angle theorem, the inscribed angle on an arc is always half of its central angle.
[tex]m\angle WXY=\dfrac{m\angle WZY}{2}[/tex]
[tex]m\angle WXY=\dfrac{118^\circ}{2}[/tex]
[tex]m\angle WXY=59^\circ[/tex]
Therefore, the correct option is A.
