Question

Point O is the center of the given circle. What is the measure of YZ?

Answer 1

Let a chord join YZ, then angle XYZ = 90° and angle XZY = 90 - 54 = 36°
angle OYZ = angle XZY = 36°

Therefore, the measure of YZ = 180 - 36 - 36 = 108°

Answer 2

Explanation:

Please refer the diagram I have attached.

Alright, lets get started.

As O is the center, OX and OY will be same because both are radius.

So, the angle OYX will also be 54 degrees.

In triangle OYZ, the angle OYZ =
`90-54=36`

As OY and OZ are same because both will be radius.

Angle YZO will also be 36 degree.

the sum of all three angles will be 180, so

Angle YOZ =
`180-36-36=108`

Hence the measure of arc YZ will be 108.

Hope it will help :)