Question

Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary. It can either be two-column or paragraph.

Answer 1

Mes ∠ O = mes (arc PQR/2)
mes ∠ Q = mes (arc POR/2)
arc PQR + arc POR = 360°
arc PQR/2 + arc POR/2 = 180°
THEN:
mes ∠ O + mes ∠ Q =  mes(arc PQR/2) + mes(arc POR/2) = 180°

∠ O + ∠ Q = 180° are supplementary