Question

Practice solving real-world angle relationship problems.
Jack is a civil engineer and 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.

What is the measure of angle BMA where the diagonals meet?

°

Answer 1

In triangle AMD the angles at A and D are 30° and 60°, so the angle at M is 180° − 30° − 60° = 90°. Since B, M, D are collinear, the angle BMA (between BM and AM) is also 90°.

Answer: 90°.