CONCEPT PREVIEW Find the measure of each central angle (in radians).

A central angle is an angle whose vertex is at the center of a circle and whose sides intersect the circle, forming an arc. The measure of a central angle corresponds directly to the length of the arc it intercepts, making it fundamental in relating angles to arc lengths.

Radians are a unit of angular measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. This unit simplifies calculations involving circles and is essential for expressing central angles in radians.

The measure of a central angle in radians is equal to the length of the intercepted arc divided by the radius of the circle (θ = s/r). Understanding this relationship allows for converting between arc length and angle measure, which is key to solving problems involving central angles.