Question

The area of a circle is 80 square inches. Find the area of the sector whose central angle is 45 degrees

Answer 1

The whole circle (in terms of area) is 360 degrees. 
Area of Sector = (angle / 360) * Area of the entire circle
Area of Sector = (45 / 360) * 80 in^2
Area of sector = (1/8) * 80 in^2
Area of sector = 10 in^2

Answer 2

We know that whole circle has 360⁰.
We can write a proportion
80 in² --------360 ⁰
x in² --------45⁰

x=(80*45)/360 =(8*45)/36 = 10 in²
The sector whose central angle is 45 degrees has are 10 in².