Geometry problem

Question

The Area of a sector of a circle with a radius measuring 15cm is 75∏ cm^{2 .} what is the measure of the central angle that forms the sector ?

Answer 1

A=∏r^2

A=∏(15)^2

A=225∏ cm^2 (area of the entire circle)

the sector has area 75∏ cm^2

75∏/225∏=1/3

the sector has area 1/3 the area of the entire circle

(1/3)(360)=120°