Angles of a Cyclic Quadrilateral

The following simulation shows a cyclic quadilateral, i.e. a quadrilateral, each of whose vertices lies on a circle.

Things to Explore

1. Drag each vertex of the quadrilateral and observe the measures of the angles.

Questions

1. If you drag one of the vertices, does the measure of the angle at this vertex change?
2. If you drag one of the vertices, does the measure of the angle at the opposite vertex change?
3. Are the measures of the opposite angles related in some way?
4. Does this relation change as you drag one of the vertices?

That’s all for this exploration. Hope you’ve discovered some interesting relations between the angles of a cyclic quadrilateral. Think about how you can formally prove what you discovered.