Thus far, in dealing with arcs and sectors, the concept of a central angle has been noted. A central angle is defined as an angle whose vertex lies at the center point of a circle. As you have seen, a central angle defines both an arc and a sector of a circle.
Another type of angle is termed an inscribed angle. An inscribed angle has its vertex on the circle itself (rather than on the center of the circle). The following diagrams illustrate the difference between a central angle and an inscribed angle:
Notice that, in the circle at the far right, there is a central angle and an inscribed angle, both of which intercept arc AXB. It is the central angle that defines the arc. That is, the arc is 60° (or one-sixth of the complete 360° circle). An inscribed angle is equal to half of the arc it intercepts, in degrees. In this case, the inscribed angle is 30°, which is half of 60°.