Question

15 the diagram below shows ∠ghi inscribed in a circle. the measure of $overset{\frown}{gi}$ is 66. what is the measure of ∠ghi?

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Apply the theorem

Given that the measure of arc $\overset{\frown}{GI}=66^{\circ}$, and $\angle GHI$ is an inscribed angle that intercepts arc $\overset{\frown}{GI}$. Let $m\angle GHI$ be the measure of $\angle GHI$. Then $m\angle GHI=\frac{1}{2}m\overset{\frown}{GI}$.

Step3: Calculate the angle measure

Substitute $m\overset{\frown}{GI} = 66^{\circ}$ into the formula: $m\angle GHI=\frac{1}{2}\times66^{\circ}=33^{\circ}$.

Answer:

$33^{\circ}$