To find the measure of a central angle, which of the following must be intercepted?

To determine the measure of a central angle in a circle, it is crucial to consider what is being intercepted by that angle. A central angle is defined as an angle whose vertex is at the center of the circle, and its rays extend out to the circumference. The portion of the circle that is "cut off" or intercepted by the rays of the angle is what we refer to as an arc.

Specifically, the measure of the central angle is equal to the measure of the intercepted arc. This connection between the angle and the arc is fundamental in circle geometry. Thus, identifying the arc that corresponds to the central angle is key to understanding its measurement.

While the other options might describe parts of a circle, they do not directly relate to the measurement of a central angle. For example, the whole circle encompasses all angles and arcs but does not specifically describe the relationship needed to find the measure of a central angle. An entire sector includes both the angle and the arc, but it is not solely what is needed to derive the angle's measure. Lastly, the radius is a line segment from the center to the circumference and does not pertain to the measurement of angles in this context.

Therefore, the arc is the essential element intercepted by the central