Given a circle with center $O$ and points $Q$, $S$, and $R$ on the circumference such that angle $QOR$ is $60°$, what is the measure of arc $QSR$ in degrees?

• A. $60°$
• B. $180°$
• C. $90°$
• D. $120°$

Answer: (A)

Verified step by step guidance

1. Identify the given elements: O is the center of the circle, and Q, S, R are points on the circumference. The angle \( \angle QOR \) at the center is given as 60°.
2. Recall the key property of circles: The measure of a central angle (an angle with its vertex at the center of the circle) is equal to the measure of the arc it intercepts.
3. Since \( \angle QOR = 60^\circ \), the arc \( QR \) intercepted by this angle also measures 60°.
4. Note that the problem asks for the measure of arc \( QSR \). Since S lies on the circumference between Q and R, arc \( QSR \) is the same as arc \( QR \) if S is on the minor arc, or it could be the major arc if S is on the opposite side.
5. Determine whether arc \( QSR \) refers to the minor or major arc. If it is the minor arc, its measure equals the central angle, which is 60°. If it is the major arc, subtract 60° from 360° to find its measure.