In a circle with center $F$, $GI$ is a diameter, and $m\angle GFH = 100^\circ$. We need to find $m\stackrel{\frown}{GH}$.

1. Problem Description

In a circle with center $F$, $GI$ is a diameter, and $m\angle GFH = 100^\circ$. We need to find $m\stackrel{\frown}{GH}$.

2. Solution Steps

The measure of a central angle is equal to the measure of its intercepted arc. Since $\angle GFH$ is a central angle, the measure of the arc it intercepts, $\stackrel{\frown}{GH}$, is equal to the measure of $\angle GFH$.

Therefore, $m\stackrel{\frown}{GH} = m\angle GFH$.

Since $m\angle GFH = 100^\circ$, we have $m\stackrel{\frown}{GH} = 100^\circ$.

3. Final Answer

100