Question

a circle has a circumference of 12. it has an arc of length 11. what is the central angle of the arc, in degrees?

Answer 1

Answer: 330⁰

Explanation:

Circumference (C) = 2π · radius(r)

12 = 2π·r

`(6)/(\pi)=r`

Arc length (s) = radius(r) · θ (reminder that theta is in radians)

`11=(6)/(\pi)\cdot \theta`

`(11\pi)/(6)=\theta`

To convert radians to degrees, use the proportion: π = 180⁰

`(\pi)/(180)=(11\pi)/(6x)\\\\6x(\pi)=180(11\pi)\\\\x=(180(11\pi))/(6\pi)\\\\x=30(11)\\\\x=330`