Answer
$m \angle{FOG}=55^{\circ} $
Work Step by Step
Now, we will use arc addition postulate to obtain:
$m \widehat{FH}=m\widehat{FG}+m\widehat{GH}$
We have $m \widehat{FH}=110^{\circ}$ and $m\widehat{GH}=m\widehat{FG}$
Thus, $110^{\circ}=2(m\widehat{FG}) \implies m\widehat{FG}=55^{\circ} $
This implies that $m \angle{FOG}=55^{\circ} $
