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

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s