Stage 18 · Circles

18.3.5 Opposite Angles of a Cyclic Quadrilateral Add to a Straight Angle

18.3 The Inscribed Angle Theorem — Seeing the World from On the Circle

Point 5 of 5

18.3.5 Opposite Angles of a Cyclic Quadrilateral Add to a Straight Angle

Core idea

In a quadrilateral with all four corners on the circle, each pair of opposite angles adds up to exactly 180 degrees.

Module goal. Introduce the inscribed angle, with its vertex on the circle, and establish its half relationship with the central angle plus a run of corollaries — this is the heart of the stage.
eastmath.com · 18.3 The Inscribed Angle Theorem — Seeing the World from On the Circle · 18.3.5 Opposite Angles of a Cyclic Quadrilateral Add to a Straight Angle