Inscribed angle measures half its intercepted arc

∠ABM = ∠CBM

∠AMB = 90

arc AB = 180

Substitution

ASA (Angle-Side-Angle)

Reflexive

Inscribed angle measures half its intercepted arc

△AMB ≅ △CMB

Circle O with diameter AB, arc AM = arc DM

The angles in a linear pair are supplementary

Given

∠CMB = 90

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

Substitution

MB = MB

∠AMB = (1/2) * arc AB

Definition