In a circle with a radius of 12, what is the measure of the central angle if the arc length is 14 pi?

The degrees will be a ratio of the arc length to the entire circumference:

Circumference = 2 x r x pi = 2 x 12 x pi = 24 pi   (360 degrees worth)

 

14pi / (24 pi)  x  360 = 210 degrees