Question

Prove that sum of opposite angle in a quadrilateral is
180

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°