In the diagram of circle A, what is the measure of ∠XYZ?

Solution:

Given, 

Measure of arc WZ = 175°

Measure of angle XAZ = 105°

We have to find the measure of angle XYZ.

We know, the angle subtended at the center is the average of the measure of arc intercepted by its angle and its vertical angles.

So, \(\frac{175°+\angle XYZ}{2}=105°\)

175° + ∠XYZ = 210°

∠XYZ = 210° - 175°

∠XYZ = 35°

Therefore, the value of ∠XYZ = 35°.

In the diagram of circle A, what is the measure of ∠XYZ?

Summary:

In the diagram of circle A, the measure of ∠XYZ is 35°.