A sector with an area of 140 pie cm^2 has a radius of 20 cm. r = 20 cm A = 140 pie cm^2 What is the central angle measure of the sector in degrees?

Question

asked Oct 19, 2021 33.7k views

2 Answers

Kenneth Lynne · Answer 1 · 2021-10-24T13:21:13+0000

Answer:

Central angle = 126°

Explanation:

Area of the sector = 140π cm²

Radius of the given circle = 20 cm

Since area of the sector =
$(\theta)/(360)* (\pi r^(2))$

[where θ is the central angle formed by the sector at the center]

140π =
$(\theta)/(360)(\pi)(20)^(2)$

θ =
$((140\pi)* 360)/(400\pi )$

θ = 126°

Therefore, central angle of the sector will be 126°.