Jack uses angle relationships to design public structures, such as buildings, bridges, and streets. He designs walking paths in a park as shown below.

Rectangle A B C D has diagonals B D and A C that intersect at the center of the rectangle at point M. Angle M A D is 30 degrees and angle M D A is 60 degrees. Angle B M A is 90 degrees.

What is the measurement of angle DMC?