Q4 of 23 Page 1

Solve Question:

Prove that. “That opposite angles of a cyclic quadrilateral are supplementary”,

Given: ABCD is a cyclic quadrilateral


To prove: ∠A + ∠C = 180° and ∠B + ∠D = 180°


Join AC and BD



∠ACB = ∠ADB - - - 1


∠BAC = ∠BDC - - 2—angle subtended by same segment


Adding 1 and 2


∴ ∠BAC + ∠ACB = ∠ADB + ∠BDC


∴ ∠BAC + ∠ACB = ∠D


∴ Adding ∠ABC to both sides


∴ ∠BAC + ∠ACB + ∠ABC = ∠D + ∠ABC


∴ 180 = ∠D + ∠ABC


∴ 180 = ∠D + ∠B


Similarly


∠A + ∠C = 180


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