How is one radian defined in terms of degrees?

One radian is defined as the angle formed when the length of the arc, subtended by the angle, is equal to the radius of the circle. This relationship is tied to the circle's total circumference, which is 2π radians or 360 degrees. In this context, one radian corresponds to approximately 57.3 degrees.

When considering the choices presented, the definition aligns with the understanding that radians and degrees are two systems for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians, making the conversion between these two measurements essential for calculations in fields like physics and engineering.

Thus, stating that one radian is equivalent to 180 degrees is a common misconception, as it is important to note that rather, π radians are equal to 180 degrees. The correct conversion focuses on how much of the circle's circumference relates back to a radian measure. Therefore, understanding that 360 degrees encompasses the entirety of a circle and that a radian does not equate directly to a fraction of this but rather is a specific value tied to the radius helps clarify the relationship between the two measurement systems.