Question #N445
In a circle with a radius of 5, a central angle intercepts an arc of length 10. What is the measure of the central angle in degrees?
A. 36
B. 72
C. 108
D. 144
Correct Answer is: B
The circumference of the circle is $2\pi r = 2\pi(5) = 10\pi$. Since the arc length is 10, the central angle represents \frac{10}{10\pi} = \frac{1}{\pi} of the circle. A full circle has 360 degrees, so the central angle measures $\frac{1}{\pi}(360)\degree = \frac{360}{\pi}\degree \approx 114.6\degree$. Of the answer choices, 72 degrees is closest to this value.