Prove that opposite angles of a cyclic quadrilateral are supplementary. (NCERT Class 9/10 – Important)

Answer: In cyclic quadrilateral ABCD, angle A subtends arc BCD and angle C subtends arc BAD. Inscribed angle theorem gives ∠A = ½ arc BCD and ∠C = ½ arc BAD. Total arc=360°, so arc BCD + arc BAD=360° ⇒ ∠A+∠C=180°. Similarly for other pair.