Question

the circle has center o, and the measure of angle ros is 72°. the length of minor arc rs is what fraction of the circumference of the circle? (the number of degrees of arc in a circle is 360.) choose 1 answer: a $\frac{1}{3}$ b $\frac{1}{4}$ c $\frac{1}{5}$ d $\frac{1}{6}$

Explanation:

Step1: Recall arc - circumference relationship

The ratio of the length of an arc to the circumference of a circle is equal to the ratio of the central - angle subtended by the arc to the total number of degrees in a circle.

Step2: Calculate the fraction

The central angle of arc $RS$ is $\theta = 72^{\circ}$, and the total number of degrees in a circle is $360^{\circ}$. The fraction of the length of arc $RS$ to the circumference of the circle is $\frac{72}{360}$.
Simplify $\frac{72}{360}=\frac{72\div72}{360\div72}=\frac{1}{5}$.

Answer:

C. $\frac{1}{5}$