What is the relation between opposite angles of cyclic quadrilateral?

The opposite angles of a cyclic quadrilateral are supplementary or their sum is 180°.  

Cyclic Quadrilateral Angles

Cyclic Quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also know as inscribed quadrilateral. The sum of the opposite angles of a cyclic quadrilateral is supplementary. 

Let ∠A, ∠B, ∠C and ∠D are the four angles of an inscribed quadrilateral. Then,

∠A + ∠C = 180° 

∠B + ∠D = 180°

Therefore, an inscribed quadrilateral also meet the angle sum property of a quadrilateral, according to which, the sum of all the angles equals 360 degrees. Hence,

∠A + ∠B + ∠C + ∠D= 360°