Answer
$m\angle E=108^{\circ}$, $m\angle F= m\angle G=72^{\circ}$
Work Step by Step
1. Given isosceles trapezoid $DEFG$ with $DE \parallel GF$, the pairs of congruent base angles will be $m\angle E=m\angle D$ and $m\angle F= m\angle G$. If $m\angle D=108^{\circ}$, then $m\angle E=108^{\circ}$.
2. The four interior angles of a quadrilateral sum to $360^{\circ}$.
$360-108-108=144$
3. Since $m\angle F= m\angle G$, the remaining 144 degrees needs to be divided equally between the two angles.
$144\div2=72$
$m\angle F= m\angle G=72^{\circ}$
