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.

$\Rightarrow m\angle XYZ = \frac{1}{2}m(ar XZ)$

$\Rightarrow 32^\circ = \frac{1}{2}m(ar XZ)$

Multiply by 2 on both sides.

$\Rightarrow 2\times 32^\circ =2\times \frac{1}{2}m(ar XZ)$

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

The measure of angle XYZ is 64°.