Question

A=m/360pi times radius to the power of 2. Given the measure m of the angle and the radius r of a circle.

Find the measure of the angle if the area of the sector is 5 square centimeters and the radius is 2 centimeters. Round your answer to the nearest tenth.

Answer 1

m = 143.2 degrees.

Answer 2

Area of a Sector

`A=(m)/(360)*\pi r^2`

• A = area of sector
• m = measure of angle in degrees
• r = radius

Solving the Question

We're given:

• A = 5 cm²
• r = 2 cm
• m = ?

Plug the given information into the equation and solve for m:

`A=(m)/(360)*\pi r^2\\\\5=(m)/(360)*\pi (2)^2\\\\5=(m)/(360)*4\pi \\\\(5)/(4\pi)=(m)/(360)\\\\m=(5*360)/(4\pi)\\\\m=143.2`

Answer

m = 143.2°