Question

Prove that opposite angles in a cyclic quadrilateral are supplementary

Answer 1

Given : Let ABCD is cyclic quadrilateral.
To prove : ∠A + ∠C = 180° and ∠B + ∠D = 180°.
Construction : join OB and OD.

Proof : ∠BOD = 2 ∠BAD
∠BAD = 1/2∠ BOD
Similarly ∠BCD = 1/2 ∠DOB
∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB
=1/2(∠ BOD + ∠DOB)
= (1/2)X360° = 180°
Similarly ∠B + ∠D = 180°