Question

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

35°
70°
75°
140°

Answer 1

Answer: the first option

Explanation:

Answer 2

Answer: First Option is correct.

Explanation:

Since we have given that

Measure of arc WZ = 175°

Measure of ∠XAZ = 105°

We need to find the measure of ∠XYZ.

As we know the angle subtended at the center is the average of the measure of arc intercepted by it angle and its vertical angles.

`(175^\circ+\angle XYZ)/(2)=105^\circ\\\\175^\circ+\angle XYZ=210^\circ\\\\\angle XYZ=210^\circ-175^\circ\\\\\angle XYZ=35^\circ`

Hence, the value of ∠XYZ is 35°.

Hence, First Option is correct.