a circle has a circumference of 20. It has an arc of length 9/2. What is the central angle of the arc in degrees?

81 degrees

Step-by-step explanation:

The circumference is given by

C = 2*pi*r

20 = 2*pi*r

Divide each side by 2pi

20/2pi = 2*pi*r/2pi

10/pi = r

We know the arc length can be found by

s = r theta where theta is in radians

9/2 = 10/pi * theta

Multiply each side by pi/10 to isolate theta

9/2 * pi/10 = pi/10 * 10/pi * theta

9*pi/20 = theta

We need to convert to degrees

9*pi/20 * 180/pi

81 degrees