Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary. It

Question

Hatshy [7]

2 years ago

8

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.

Mathematics

1 answer:

11111nata11111 [884] · Answer 1 · 2022-01-06T20:19:55+03:00

11111nata11111 [884]2 years ago

6 0

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