Question

What is the measure of arc GH??

Answer 1

Option C:

The measure of arc GH is 45°.

Solution:

Given data:

m∠GFH = 22.5°

To find the measure of arc GH:

By inscribed angle theorem,

The measure of an inscribed angle is equal to the half of the measure of the intercepted arc.

$m\angle GFH = \frac{1}{2}\times m \ {(arc \ GH)}$

$22.5^\circ= \frac{1}{2}\times m \ {(arc \ GH)}$

Multiply by 2 on both sides, we get

$2\times 22.5^\circ= 2\times \frac{1}{2}\times m \ {(arc \ GH)}$

$45^\circ= m \ {(arc \ GH)}$

Switch the sides.

m(arc GH) = 45°

The measure of arc GH is 45°.

Option C is the correct answer.