1. what is a central angle and what is the relationship of the central angle and the intercepted arc?

2. what is an inscribed angle and what is the relationship of the inscribed angle and the intercepted arc?

3. find the value of x in the figure below. show all steps.
(left image)

4. find the value of x in the figure below. show all steps.
(right image)

1. Well for a circle, a central angle is formed by two radii.  A central angle is an angle with endpoints which is located on a circle's circumference and vertex which is located on a circle's center. So the measure of the central angle is equal to the measure of the intercepting arc.

2. An inscribed angle is an angle that is formed by two chords that meet at the same point on a circle. The measure of an inscribed angle is 1/2 the measure of its intercepted arc.

I think you could handle the rest of this problem hope it all helped!