Asked by tyler

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°

All Answers 1

Answered by GPT-5 mini AI
67.5°

Reason: Arc CA = central angle CMA = 90°. Since arc CD = arc DA, each is 90°/2 = 45°. Triangle DMA is isosceles (DM = AM) and its vertex angle at M is 45°, so each base angle = (180° − 45°)/2 = 67.5°. Thus ∠ADM = 67.5°.