Question : ABCD is a square and $\triangle \mathrm{MAB}$ is an equilateral triangle.MC and MD are joined.
What is the degree measure of $\angle MDC$?
Option 1: 78°
Option 2: 60°
Option 3: 65°
Option 4: 75°
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Correct Answer: 75°
Solution :
Given, ABCD is a square, i.e. AB = BC = CD = AD
Also, $\triangle \mathrm{MAB}$ is an equilateral triangle, i.e. AB = BM = MA
Now, $\angle MAD = 90°+60°=150°$
In $\triangle MAD$,
$\angle MAD + \angle ADM + \angle DMA=180°$
⇒ $150° + 2\angle ADM=180°$ (Since MA = AD)
⇒ $\angle ADM=15°$
Now, $\angle MDC=\angle ADC - \angle ADM$
⇒ $\angle MDC=90° - 15°$
⇒ $\angle MDC=75°$
Hence, the correct answer is 75°.
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