arc cd is $\frac{1}{4}$ of the circumference of a circle. what is the radian measure of the central…

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

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

Answer

Explanation:

Step1: Recall radian - arc - circle relationship

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

Step2: Calculate the central - angle measure

If an arc is $\frac{1}{4}$ of the circumference of a circle, the central angle corresponding to this arc is $\frac{1}{4}$ of the total radian measure of the circle. So the central - angle measure $\theta=\frac{1}{4}\times2\pi$. $\theta = \frac{\pi}{2}$ radians.

Answer:

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