Use the theorems that you that you have learned about inscribed angles and intercepted arcs to explain why inscribed quadrilaterals have opposite angles that are supplementary. Answer in 5-6 lines.

Answer 1

Since you have learned about inscribed angles and intercepted arcs, it is safe to assume that you are familiar with what they are.

Following is a summary of hints to help complete the proof.

fact #1: the sum of the intercepted arcs of the sides of a cyclic quadrilateral (a quad inscribed in a circle) adds up to 360°. Draw a sketch to convince yourself of this fact.

fact #2: The inscribed angle subtended by each side is exactly half the intercepted arc subtended by the same side.

The final step:
Draw a quad inscribed in a circle, then draw exactly one diagonal. Now identify all the inscribed angles, and determine what the sum of the four angles are, using facts 1 and 2.

If you need to review what inscribed angles and intercepted arcs are, try
http://www.onlinemathlearning.com/arc-angles.html
or
http://www.mathopenref.com/arcintercepted.html