What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a 12pi centimeters arc?

Step-by-step explanation:

We'll use s = rt where s is arc length, r is the radius, and t is the angle in radians. After we find the angle in radians, we'll convert it to degrees to get the central angle.

so

That's the arc length in radians. Radians does not measure the central angle so we convert using the fact that pi is the same as 180 degrees:

The pi's cancel out and 3 goes into 180 60 times, and 60 times 2 is 120, so the angle measure in degrees is 120