While on vacation at the beach, Eleanor drew the figure shown.

Question

In Eleanor's drawing, the measure of ∠FMD
is 15°, and the measure of ∠BMC
is 30°.
What is the measure of ∠CMD
? 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.

(1 point)
degrees

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Answer 1

To find the measure of ∠CMD, we can follow the relationship of the angles that are given.

1. We know that angle BMF is divided into three angles: ∠BMC, ∠CMD, and ∠DMF.
2. Since angle AMB and angle BMF are both right angles, angle BMF measures 90 degrees.

We can use the following information:

• ∠BMC = 30°
• ∠DMF = 15° (since it is equal to ∠FMD)

Now, we can calculate ∠CMD using the equation: \[ \text{∠BMF} = \text{∠BMC} + \text{∠CMD} + \text{∠DMF} \]

Substituting the known values: \[ 90° = 30° + \text{∠CMD} + 15° \] Combining the known angles on the right side gives: \[ 90° = 45° + \text{∠CMD} \]

Now, to isolate ∠CMD, subtract 45° from both sides: \[ \text{∠CMD} = 90° - 45° \] \[ \text{∠CMD} = 45° \]

So, the measure of ∠CMD is 45 degrees.