Question

A circle has a circumference of 12 it has an arc of length 11 what is the central angle of the arc in degreesA 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:

330°

Step-by-step explanation:

The central angle:

360°×$\frac{11}{12}$

=30°×11

=330°

Answer 2

Answer:   330⁰

Step-by-step explanation:

Circumference (C) = 2π · radius(r)

                          12 = 2π·r

                     $\dfrac{6}{\pi}=r$

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

                  $11=\dfrac{6}{\pi}\cdot \theta$

                  $\dfrac{11\pi}{6}=\theta$

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

$\dfrac{\pi}{180}=\dfrac{11\pi}{6x}\\\\6x(\pi)=180(11\pi)\\\\x=\dfrac{180(11\pi)}{6\pi}\\\\x=30(11)\\\\x=330$