Question 69
In triangle $ABC$, $\angle A = 50^\circ$, $\angle B = 60^\circ$, and $\angle C = 70^\circ$. A ray of light bounces from point $D$ on $BC$ to $E$ on $CA$ to $F$ on $AB$ and then back to $D$. Find the angles of $\triangle DEF$.
(Light always takes the shortest path between points, meaning it bounces off an edge at equal angles.)
(Light always takes the shortest path between points, meaning it bounces off an edge at equal angles.)