Inscribed Angles (Angles on a Circles Edge)

Angles, Circle
The pink angle is said to be an inscribed angle within the circle below. This inscribed angle intercepts the thick blue arc of the circle. Because of this, this thick blue arc is said to be the inscribed angle's intercepted arc. Notice how the blue central angle also intercepts this same thick blue arc. To start: 1) Move point D wherever you'd like. 2) Adjust the size of the thick blue intercepted arc by moving the other 2 blue points (if you wish.) 3) Click the checkbox to lock point D. 4) Follow the interactive prompts that will appear in the applet. Interact with the following applet for a few minutes. Then, answer the questions that follow.

How many pink inscribed angles fill a central angle that intercepts the same arc?

What does the measure of an central angle (of a circle) measure? How doe sthis compare with the arc it intercepts?

Given your responses to (1) and (2) above, how would you describe the relationship between the measure of an inscribed angle (of a circle) with respect to the measure of a central angle, provided they intercept the same arc?

Slide the gray tool to the right and notice what happens. Change the length of the blue intercepted arc and see what happens to the measures of the pink inscribed angles.
Play with the app to discover the relationship between opposite angles in an inscribed quadrilateral in a circle.

What can you say about the measure of opposite angles in an inscribed quadrilateral?