Prove that the opposite angles of a cyclic quadrilateral are supplementry.

please provide a complete proof ......................??????

We have to prove that the opposite angles of a cyclic quadrilateral are supplementary.

Proof- Since we know that angle subtended by an arc at the centre is double to that of the any part of the circle.

So,

 ......(1)

Similarly,

 .......(2)

Combining equation (1) and (2) to get,

Hence you can prove the other part as well.