Measure of angle problem

Question

A circle with a circumference of 432 cm is centered at the vertex of an angle, and the angle's rays subtend an arc that is 306 cm long. What is the measure of this angle in degrees?

Answer 1

432 = pi(d) = (pi)(2r)

216 = pi(r)

r = 216/pi = the radius of the circle

radians times radius = arc length = 306

angle in radians = 306/(216/pi) = 306pi/216

= 153pi/108 = 17pi/12 = (17/12)pi radians

convert to degrees, multiply by 180/pi

= (17/12)pi x 180/pi = 17/12 x 180 = 17(15) = 255 degrees