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


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


About mvtrinh

Retired high school math teacher.
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