A central angle is an angle with its vertex at the center of a circle:

 a. If the central angle cuts off a quarter-circle, what is the measure of the central angle? b. If the central angle cuts off a semicircle, what is the measure of the central angle? c. If the central angle cuts off one-third of a circle, what is the measure of the central angle? d. Find a general rule for central angles based on how much of the circle they cut off.

 a. The measure is 90° (or 360° / 4). b. The measure is 180° (or 360° / 2). c. The measure is 120° (or 360° / 3). d. If a central angle cuts off an arc of one n-th of the full circle, its measure is 360° / n.

Central Angle:
A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle.

 Central Angle = Intercepted Arc

<AOB is a central angle.
Its intercepted arc is the minor arc from A to B.  m<AOB = 80º

Inscribed Angle:
An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

 Inscribed Angle = Intercepted Arc

<ABC is an inscribed angle.
Its intercepted arc is the minor arc from A to C.
m<ABC = 50º