Math, asked by anjali255, 1 year ago

prove that the opposite angle of a cyclic quadrilateral are supplementary

Answers

Answered by janhvivd16
30

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Answered by Anonymous
14

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°

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