Final answer:
An angle that turns through 1/360 of a circle measures 1 degree, as a full circle is comprised of 360 degrees. This angle can also be expressed in radians as π/180 radians.
Step-by-step explanation:
When an angle turns through 1/360 of a circle, it is making a rotation equivalent to one degree. This is because a full circle is defined as consisting of 360 degrees. Therefore, if we divide the circle into 360 equal parts, each part corresponds to an angle of 1 degree. To measure larger angles, we simply add up these single-degree increments.
Alternatively, we could express this angle in radians. Since one revolution (360 degrees) equals 2π radians, one degree is therefore equal to 2π/360 radians, or π/180 radians. Consequently, the angle of 1/360 of a revolution, or one degree, corresponds to π/180 radians. If we need to measure angular velocity or convert between different units like degrees and radians, the formulas provided can be used for precise calculations.