## Elementary Geometry for College Students (6th Edition)

$m\angle$$D = 75$$^{\circ}$ $m\angle$$DEF = 125$$^{\circ}$
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}$.