While on vacation at the beach, Eleanor drew the figure shown.
In Eleanor's drawing, the measure of
∠
F
M
D
is 15°, and the measure of
∠
B
M
C
is 30°.
What is the measure of
∠
C
M
D
? Enter your answer in the box.
Angle AMB and angle BMF are right angles with common side BM. Segment MC and MD divide angle BMF into 3 angles; angle BMC, angle CMD and angle DMF.
degrees
4 / 19
We can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle BMC.
Angle AMB is 90 degrees and angle BMF is 90 degrees, so the measure of angle AMF is 180 - 90 - 90 = 0 degrees.
Since angles BMC, CMD, and DMF divide angle BMF into three parts, their measures must add up to 90 degrees. We know that angle CMD is 15 degrees (given) and angle BMF is 90 degrees, so angle BMC + angle DMF = 90 - 15 = 75 degrees.
Now we can use the fact that angle BMC + angle BMF + angle CMB = 180 degrees to find the measure of angle BMC. We know that angle BMF is 90 degrees and angle CMB is 30 degrees (given), so angle BMC + 90 + 30 = 180 degrees, which means angle BMC = 60 degrees.
Finally, we can find the measure of angle CMD by using the fact that angles BMC, CMD, and DMF add up to 75 degrees. We know that angle BMC is 60 degrees and angle CMD is 15 degrees, so angle DMF = 75 - 60 - 15 = 0 degrees.
Therefore, the measure of angle CMD is 15 degrees.