Question

Prove the opposite angle of cyclic quadrilateral are supplementary ​

Answer 1

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Answer 2

Answer:

❀given:

let ABCD is cyclic quadrilateral

❀ To Prove:

∠A+ ∠C=180° and ∠B+∠D=180°

❀proof:

∠BOD=2 ∠BAD

∠BAD=$\frac{1}{2}$∠BOD

Similarly ∠BCD=$\frac{1}{2}$∠DOB

∠BAD +∠BCD=$\frac{1}{2}$∠BOD+$\frac{1}{2}$∠DOB

=$\frac{1}{2}$(∠BOD+∠DOB)

=($\frac{1}{2} )$×360°=180°

similarly ∠B+∠D=180°