If an angle in standard position intercepts an arc of a unit circle with a measure of $64°$, what is the measure of the arc in degrees?

• A. $92°$
• B. $50°$
• C. $64°$
• D. $44°$

Answer: (C)

Verified step by step guidance

1. Understand that the problem involves an angle in standard position intercepting an arc on a unit circle. The measure of the intercepted arc in degrees is directly related to the measure of the central angle in degrees.
2. Recall the key property of a unit circle: the measure of an arc intercepted by a central angle is equal to the measure of that angle in degrees.
3. Since the angle given is 64 degrees, the intercepted arc on the unit circle will also measure 64 degrees.
4. No additional calculations are needed because the unit circle radius is 1, and the arc length in degrees corresponds exactly to the angle measure.
5. Therefore, the measure of the arc intercepted by the angle is the same as the angle measure, which is 64 degrees.