#### Answer

Yes.
$m\angle EHG=\frac{1}{2}($measure of arc $EG +$ measure of arc $DF)$

#### Work Step by Step

$m\angle EHG=\frac{1}{2}($measure of arc $EG +$ measure of arc $DF)$
Substituting in known values from previous parts...
$93=\frac{1}{2}(EG+104)$
Multiply both sides by 2 (to clear the fraction)...
$186=EG+104$
Subtracting 104 from both sides...
$82=EG$
So the question now is...does the measure of arc $EG=82^{\circ}$?
Yes. The measure of a central angle is equal to the measure of its intercepted arc. We are given that the $m\angle EOG=82^{\circ}$, therefore the measure of its intercepted arc (arc $EG$) equals $82^{\circ}$.