Opposite Angles of a Cyclic Quadrilateral are Supplementary

This GeoGebra example dynamically demonstrates the theorem that opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) are supplementary, meaning their sum is 180 degrees. The core mathematical concepts involve circles, inscribed angles, the inscribed angle theorem, and angle sum properties of quadrilaterals. The construction uses the Circle command to create circle O, places points A, B, C, D on the circle, connects them with Segment commands to form the quadrilateral, and uses Angle commands to label interior angles α, β, γ, etc. Additional Ray and auxiliary points (E, f) help construct related angles, and a text object displays the angle measures. This is suitable for middle school geometry lessons to explore the relationship between inscribed angles and circle properties, and for high school review of cyclic quadrilateral criteria. Users can drag vertices to observe how angles change while the supplementary relationship remains invariant, reinforcing the theorem through interactive exploration.