Angles in a cyclic quadrilateral

A cyclic quadrilateral is one whose corners all lie on the circumference of a circle.

Opposite angles are supplementary (ie add up to 180°).

Try moving the points and confirming this.

Notice that when it ceases to be a quadrilateral (ie the sides cross each other) we have an example of angles in the same segment (although the chord is not shown).

To download this Geogebra file click here.