Fourth circle theorem: 'Angles in a Cyclic Quadrilateral'

Angles in a Cyclic Quadrilateral

Fourth circle theorem:

What's the connection between pairs of opposite angles (α and γ or β and δ)?  ***

You can use the cursor to move any of points A, B, C or D around the circumference, and hence alter some of the angles.
You can also move point X or O to change the size of the circle.

*** Hint: Add the pair of angles!

If you need it, this theorem is set out here

and all the theorems are summarised here

Tim Devereux, Created with GeoGebra