Provethat the opposite sides of a cyclic quadrilateral are supplementa

1.	Provethat the opposite sides of a cyclic quadrilateral are supplementary
Answer» 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° Like my answer if you find it useful!

Provethat the opposite sides of a cyclic quadrilateral are supplementary

Answer»

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°

Like my answer if you find it useful!