Question

The measure of arc XZ is 32°.

What is the measure of XYZ?
A. 32°
B. 64°
C. 148°
D. 16°

Answer 1

Given:

Measure of arc XZ = 32°

To find:

The measure of XYZ

Solution:

The measure of inscribed angle is half of the measure of the intercepted arc.

`$\Rightarrow m\angle XYZ = (1)/(2)m(ar XZ)`

`$\Rightarrow 32^\circ = (1)/(2)m(ar XZ)`

Multiply by 2 on both sides.

`$\Rightarrow 2* 32^\circ =2* (1)/(2)m(ar XZ)`

`$\Rightarrow 64^\circ =m(ar XZ)`

The measure of angle XYZ is 64°.