Question

prove that the opposite angle of cyclic quadrilateral are supplementary ​

Answer 1

Sol : 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°

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