A happy and successful New Year!

I've modified your drawing a little bit:

1. The points A, E, D, B are located on the circumference of a circle around M.

2. The angles and the subtend the same cord of the circle. Thus they must be equal.

3. is the center angle of the the angles of #2. Therefore

to #c) You can prove that the triangles in question are congruent and therefore the angles in question must be equal.