Answer
$m\angle$$D$ = $75$$^{\circ}$
$m\angle$$DEF$ = $125$$^{\circ}$
Work Step by Step
We arrive at these answers by assuming that $\triangle$$ABC$ and $\triangle$$CDE$ are similar triangles, which makes their angles congruent and their sides proportional. By making this assumption we are able to assume that $M\angle$$D$ equals $75$$^{\circ}$ which makes the sum of $\angle$$D$ and $\angle$$C$ $125$$^{\circ}$. This leaves the last interior angle ( $\angle$$E$ ) equal to $180$$^{\circ}$ - $125$$^{\circ}$ which equals $55$$^{\circ}$. Therefore the $m\angle$$E$ = $55$$^{\circ}$. This allows us to find out the $m\angle$$DEF$. By taking the difference of $m\angle$$E$ and $180$$^{\circ}$. Which leaves us with the $m\angle$$DEF$ = $125$$^{\circ}$.
