Opposite angles of a cyclic quadrilateral are supplementary

Dependencies: Central angle is twice the inscribed angle on the same arc.

Statement

Let quadrilateral $ABCD$ be inscribed in a circle $\odot O$ (i.e. its four vertices all lie on the circle, ordered around the circle in sequence). Then any pair of opposite angles sums to $180^\circ$:

Equivalently — pick any exterior angle, and the exterior angle = the opposite interior angle (the non-adjacent one). This is the "supplementary opposite angles" theorem for cyclic quadrilaterals, and it is also one of the most-used criteria for determining whether four points are concyclic.