Question

if ∠def measures 60°, what is the measure of ⁀df? a. 30° b. 120° c. 60° d. 300°

Explanation:

Step1: Recall central - angle arc relationship

The measure of an arc of a circle is equal to the measure of the central angle that intercepts it.

Step2: Identify the central angle

Here, $\angle DEF$ is a central angle of the circle with center $E$, and it intercepts the arc $\overset{\frown}{DF}$. Given that $\angle DEF = 60^{\circ}$.

Step3: Determine the arc measure

Since the measure of arc $\overset{\frown}{DF}$ is equal to the measure of central - angle $\angle DEF$, the measure of $\overset{\frown}{DF}$ is $60^{\circ}$.

Answer:

C. $60^{\circ}$