<AMB = 90

Substitution

<ABM = (1/2) * arc AM and <CBM = (1/2) * arc DM

<ABM = <CBM

<CMB = 90

Inscribed angle measures half its intercepted arc

Circle O with diameter AB, arc AM = arc DM

Substitution

The angles in a linear pair are supplementary

Given

arc AB = 180

Triangle AMB is congruent to Triangle CMB

ASA (Angle-Side-Angle)

Reflexive

Inscribed angle measures half its intercepted arc

MB = MB

<AMB = (1/2) * arc AB

Definition