Question 48
In a triangle $ABC$, the external bisector of $\angle BAC$ intersects the ray $[BC$ at $D$. The feet of the perpendiculars from $B$ and $C$ to the line $AD$ are $E$ and $F$ respectively, and the foot of the perpendicular from $D$ to $AC$ is $G$. Show that $\angle DGE + \angle DGF = 180^\circ$.