Question

A circle with a radius of 12 inches has an arc that measures 8 pi inches. Find the measure of the central angle determined by this arc.

Answer 1

we know that

[length of a circle]=2*pi*r
r=12 in
[length of a circle]=2*pi*12--------------> 24pi in

if 360° (full circle)--------------------> has a length of 24pi in
X-------------------------------------------> 8pi

X=8pi*360/24pi-----------> 120°

the answer is 120°