Question

prove that opposite angles of cyclic quadrilateral are supplementary​

Answer 1

Given:- ABCD is a Cyclic Quadrilateral

To prove:- ∠A + ∠C = 180° & ∠B + ∠D = 180°

Construction:- Join OB & OD

To Proof:- ∠BOD = ∠2BAD

=> ∠BAD = 1/2 ∠BOD

Similarly∠BCD = 1/2 ∠DOB + ∠BAD + ∠BCD =1/2

∠BOD + 1/2 ∠DOB =1/2 (∠BOD + ∠DOB)

=> 1/2 × 360° = 180°

Similarly ∠B + ∠D = 180°

Hence Proved

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°