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.