Measure of Angle

Let $ABCD$ be a rectangle with $BC=2AB$, and let $BCE$ be an equilateral triangle. $\overline{BE}$ and $\overline{EC}$ intersecting $\overline{AD}$ (not the extension of $\overline{AD}$) at $F$ and $G$, respectively. If $M$ is the midpoint of $\overline{EC}$, how many degrees are in angle $CMD$?
Source: NCTM Mathematics Teacher 2006

SOLUTION

$m\angle MCD=90-60=30^\circ$
Triangle $CMD$ is isosceles because $CM=CD=BC/2$
$m\angle CMD=(180-30)/2=150/2=75^\circ$

Answer: $75^\circ$