In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.
Proof
Let two equal circles have equal central angles ∠BAC and
∠EDF. In radius-chord-radius triangles △ABC and
△DEF: AB=AC=DE=DF (equal radii, equal circles)
and ∠BAC=∠EDF (given); by SAS (I.4) the triangles
are congruent and the chords BC=EF. Equal chords in equal
circles subtend equal arcs (by superposition). For inscribed
angles, double them via III.20 to reduce to the central-angle case.