What unit of angle is equal to the angle at the center of a circle whose arc is equal in length to the radius?

The unit of angle that is equal to the angle at the center of a circle when the length of the arc is equal to the radius is the radian. In a circular measurement, the radian is defined based on the radius of the circle. Specifically, when the arc length is equal to the radius, the corresponding angle at the center of the circle measures one radian. This relationship establishes a direct connection between linear measurement along the circumference and angular measurement at the center, which is intrinsic to the definition of radians.

In contrast, degrees are a different system of measuring angles and do not relate directly to the radius and arc length in the same way. An arcminute is a subdivision of degrees and further divides an angle into smaller units, while a steradian is used for measuring angles in three-dimensional space, specifically in a sphere, rather than in a circle. Therefore, the radian serves as the fundamental unit in this context due to its derivation from the properties of circles.