Problem: To prove that opposite angles of an inscribed quadrilateral are supplementary.
First construct a circle.
Next, add four points anywhere on the circle. Construct segments to create your inscribed quadrilateral.
Measure angle DAB and measure the opposite angle, which is angle DCB.
Angle DAB and angle DCB add up to 180 degrees. Therefore they are supplemental angles. Angle DAB is half of arc BCD and angle DCB is half of arc BAD. In conclusion, anytime you have an inscribed quadrilateral (inside a circle), your angles will be supplementary.