13.7k views
1 vote
The measure of arc XZ is 32°.

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

The measure of arc XZ is 32°. What is the measure of XYZ? A. 32° B. 64° C. 148° D-example-1
User Elle Mundy
by
5.8k points

1 Answer

4 votes

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°.

User Roohul
by
5.0k points