ABCD is a square and ΔMAB is an equilateral triangle. MC and MD are joined. What is the degree measure of ∠MDC?

Solution (By Examveda Team)

∠A = ∠B = ∠D = ∠C = 90°
ΔAMB is equilateral
Hence ∠A = 60°
∠DAM = 90° + 60° = 150°
∠ADM $$ = \frac{{{{180}^ \circ } - {{150}^ \circ }}}{2} = \frac{{{{30}^ \circ }}}{2} = {15^ \circ }$$
∠MDC = 90° - 15° = 75°