What is the measure of angle WZY?
54.5°, 71°, 125.5°, 180°

Solution:

The lines ZY and ZW are tangents to the circle which is centered at x.

As per the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle.

I.e. XW and ZY respectively.

As evident from the above diagram, angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Of the four angles of the quadrilateral, the three angles are 109°, 90°, 90°. Hence the fourth angle i.e.

∠WZY = 360° - 90° - 90° - 109°

∠WZY = 71°

What is the measure of angle WZY?

Summary:

The measure of angle WZY is 71°.