Question

how to prove that the sum of 2 opposite angle is 180 degree in a cyclic quadrilateral.

Answer 1

Theorem of cyclic quadrilateral:opposite angles of cyclic quadrilateral are supplementary

Answer 2

Hey mate,

Sol : 

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°

hope this helps you out!