Inscribed Quadrilateral Property
Definition

Opposite angles in an inscribed quadrilateral are supplementary.

Example

In the figures below, angleA and angleB are supplementary (add up to 180°), since they are opposite angles of an inscribed quadrilateral.

Inscribed Quadrilateral Angle Example

In the figures above, angleC and angleD are supplementary (add up to 180°), since they are opposite angles of an inscribed quadrilateral.

Demonstration
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Explanation

Click here for an mathematical explanation of WHY the Inscribed Quadrilateral Property works.

Note that this is not a PROOF but an EXPLANATION.