Answer
$235^{\circ}$
Work Step by Step
In order to compute the arc measurement, we must recall the following points
A) The measure of a semi-circle arc is equal to $180^{\circ}$
B) The measure of a minor arc is equal to the measure of its corresponding central angle.
C) The measure of a major arc is equal to the measure of the related minor arc subtracted from the angle $360^{\circ}$.
We will use arc addition postulate to obtain:
$m \widehat{JEG}=m\widehat{JEF}+m\widehat{FG}$
We can see that $\widehat{FHJ}$ is a semi-circle and $m \widehat{FG}=55^{\circ}$
So, $m\widehat{JEG}=180^{\circ}+55^{\circ}$
or, $m\widehat{JEG}=235^{\circ}$
