Question

Circle X is shown. Line segments W X and Y X are radii. Tangents W Z and Y Z intersect at point Z outside of the circle. Arc W Y is 109 degrees.

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

Answer 1

From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°

How to find the angle from a circle tangent?

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

From 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.

From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;

∠WZY = 360° - (90° + 90° + 109°)

∠WZY = 360° - 289°

∠WZY = 71°

Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°

Read more about Angle from a Circle Tangent at; https://brainly.com/question/15890932

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