Same segments and cyclic quadrilaterals

Angles subtended by the same chord at points on the same side of the chord are equal. Sharing a chord alone is insufficient: points on opposite sides give supplementary angles.

A cyclic quadrilateral has all four vertices on one circle. Its opposite angles sum to 180°. An exterior angle equals the opposite interior angle.

State the cyclic order: in cyclic quadrilateral \(PQRS\), \(\angle PQR\) and \(\angle PSR\) are opposite. A diagram alone does not justify assuming that an unspecified quadrilateral is cyclic.