The sum of either pair of opposite angles of a cyclic quadrilateral is `180^0` OR The opposite angles of a cyclic quadrilateral are supplementary.

Explanation

Proof `:` `/_DAB` is inscribed in arc DAB and intercepts arc DCB
`:. /_DAB = (1)/(2)` m ( arc DCB ) ….(Inscribed angle theorem ) …(1)
`/_DCB ` is inscribed in arc DCB and intercepts arc DAB
`:. /_DCB = (1)/(2)` m ( arc DAB ) ....(Inscribed angle theorem ) ...(2)
Adding (1) and (2) , we get ,
`/_DAB + /_DCB = (1)/(2) `m (arc DCB ) `+ (1)/(2) ` m (arc DAB )
`:. /_DAB + /_DCB = (1)/(2)` m (arc DCB ) `+` m (arc DAB )
Arc DCB and arc DAB constitute a complete circle
`:. /_DAB + /_DCB = (1)/(2) xx 360^(@)` ....(Measure of a circle is `360^(@)`)
`:. /_DAB + /_DCB = 180^(@)`
Similarly, we can prove , `/_ABC + /_ADC = 180^(@)`