Question

prove that opposite angle of cyclic quadrilateral are supplementary

Answer 1

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°

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°