KöMaL 2010 B4240

The planes $S_1$ and $S_2$ intersect in a line $m$. Line $e$ intersects plane $S_i$ at the point $D_i$. The angle enclosed by $e$ and $S_i$ is $\alpha_i$. Show that if $D_1 \ne D_2$, then $\alpha_1$>$\alpha_2$ holds true if and only if $D_1$ lies closer to $m$ than $D_2$.