Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.
Relate inscribed angles to intercepted arcs
Problem
Inscribed angle \(\angle~ABC\) intercepts \(\text{minor}~\text{arc}~AC\), whose measure is \(124°\). Apply the inscribed-angle theorem to calculate \(m\angle~ABC\) and state the arc-to-angle relationship used.
For an inscribed angle, the two chord endpoints determine the intercepted arc opposite the vertex. We’ll preserve that endpoint pairing, confirm that the vertex lies on the circle, and apply the half-arc relationship before checking the result in reverse.
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