Question

arc cd is $\frac{1}{4}$ of the circumference of a circle. what is the radian measure of the central angle? $\frac{pi}{2}$ radians $4pi$ radians $\frac{pi}{4}$ radians $2pi$ radians

Explanation:

Step1: Recall full - circle radian measure

The radian measure of a full - circle is $2\pi$ radians.

Step2: Calculate the central angle

Since arc CD is $\frac{1}{4}$ of the circumference, the central angle $\theta$ corresponding to arc CD is $\frac{1}{4}$ of the full - circle's radian measure. So, $\theta=\frac{1}{4}\times2\pi$.
$\theta = \frac{\pi}{2}$ radians

Answer:

$\frac{\pi}{2}$ radians