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°