We are given a circle with center F. The central angle $angle GFH$ measures $100^\circ$. We need to find the measure of the major arc $GJH$.

1. Problem Description

We are given a circle with center F. The central angle $angle GFH$ measures $100^\circ$. We need to find the measure of the major arc $GJH$.

2. Solution Steps

The measure of a full circle is $360^\circ$.

The measure of arc $GH$ is equal to the measure of the central angle $angle GFH$, which is given as $100^\circ$.

Therefore, $m \stackrel{\frown}{GH} = 100^\circ$.

The major arc $GJH$ is the rest of the circle besides the minor arc $GH$.

Thus, the measure of major arc $GJH$ is the difference between the full circle ($360^\circ$) and the minor arc $GH$ ($100^\circ$).

$m \stackrel{\frown}{GJH} = 360^\circ - m \stackrel{\frown}{GH}$

$m \stackrel{\frown}{GJH} = 360^\circ - 100^\circ$

$m \stackrel{\frown}{GJH} = 260^\circ$

3. Final Answer

260