In an inscribed quadrilateral, also known as a cyclic quadrilateral, the opposite angles are supplementary, meaning that the sum of each pair of opposite angles equals 180 degrees. This relationship arises from the fact that each angle is subtended by arcs of the circle formed by the other two vertices. Thus, if angles A and C are opposite, and angles B and D are also opposite, we have A + C = 180° and B + D = 180°.
Quadrilateral upper Q upper U upper A upper D is drawn within a circle such that all vertices touch the edge of the circle.
A quadrilateral is inscribed in a circle. Explain in 2-3 sentences how the opposite angles of an inscribed quadrilateral are related.
1 answer