A circle has an arc of length 24π that is intercepted by a central angle of 80°. What is the radius of the circle?

In a circle, arc length = the degree multiplied by the radius.

Now we need to substitute in the given numbers

24 (pi) = 80 * x (given that the radius is x)

Solve like a normal algebra problem.

To get x by itself, we divide 24 (pi) by 80 which gives us

X = 0.9424

I got radius = 54

arc/2pi r = degrees/360

then fill in what you know: 24pi/2pi r = 80/360

Now cross multiply and you get: 8640pi = 160pi r

Now divide both sides by 160pi and you get: 54 = r