If a quadrilateral has one pair of opposite angles that add to 180, then you know it is cyclic. A trapezoid is cyclic if, and only if, it is isosceles.
There exist several interesting properties about a cyclic quadrilateral.
All the four vertices of a quadrilateral inscribed in a circle lie on the circumference of the circle.
The sum of two opposite angles in a cyclic quadrilateral is equal to 180 degrees (supplementary angles)
A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle.
If an exterior angle of a quadrilateral is equal to the interior opposite angle then the quadrilateral is a cyclic quadrilateral.
