Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA. Circle M is shown. Line segment B D is a diameter. LIne segments E M and A M are radii. Lines are drawn from points C and A to point D to form chords. A line is also drawn from point C to point A. Angle C M A is 90 degrees. Arcs C B and B A are congruent.

What is the measure of angle ADM?

22.5°
30.0°
45.0°
67.5°