Prove that sum of opposite angles of a cyclic quadrilateral is 180

1.	Prove that sum of opposite angles of a cyclic quadrilateral is 180
Answer» ANSWER: 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∠ BODSimilarly ∠BCD = 1/2 ∠DOB ∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB =1/2(∠ BOD + ∠DOB) = (1/2)X360° = 180° Similarly ∠B + ∠D = 180°

Answer»

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∠ BODSimilarly ∠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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Prove that sum of opposite angles of a cyclic quadrilateral is 180

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