ABCD is a square and ΔMAB is an equilateral triangle. MC and MD are joined. What is the degree measure of ∠MDC ?
Answer & explanation
Correct answer: option 4
ABCD is a square, = AB = BC = CD = DA
MAB is an equilateral triangle, = MA = AB = BM
square ABCD and equilateral triangle MAB have a common side AB.
= AB = BC = CD = DA = MA = MB
In △MAD,
= MA = DA
∠ADM = ∠AMD = x
With ∠DAM
= ∠DAM = ∠MAB + ∠DAB
= ∠DAM = 90° + 60°
= ∠DAM = 150°
Sum of angles of triangle MAD = 180°
= ∠DAM + ∠AMD + ∠ADM = 180°
= 150° + x + x = 180°
= 2x = 180° - 150°
= x = 15°
Hence, ∠ADM = ∠BCM = 15°
Now for ∠MDC, = ∠MDC = ∠ADC - ∠ADM
= ∠MDC = 90° - 15° = 75°