Question

What is the measure of XYZ

Answer 1

The answer is 93. The angle looks really close to 90 and 93 is the closest.

Answer 2

Option C is correct.

Explanation:

Given: a measure of Angle = 186°

To find: measure of the ∠XYZ.

We know that given measure of the angle is the angle made by the arc at the center.

⇒ reflex of m∠XOZ = 186°

Figure is attached with required construction.

We use a result which states that the angle subtended by arc at the center is double the angle subtended by it at any point on the remaining part of the angle.

XZ is Major arc.

So we have,

⇒ reflex of ∠XOZ = 2 ∠XYZ

186 = 2∠XYZ

∠XYZ = 93°

Therefore, Option C is correct.