Question

Prove the following theorem.
The sum of either pair of opposite angles of a quadrilateral is 180°

Answer 1

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Answer 2

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°