Question

A sector with an area of \goldE{140\pi\,\text{cm}^2}140πcm

2
start color #a75a05, 140, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{20\,\text{cm}}20cmstart color #ca337c, 20, start text, c, m, end text, end color #ca337c.



What is the central angle measure of the sector in degrees?

Answer 1

I got it right. 108

Explanation:

Answer 2

The central angle of the sector is 126°.

Explanation:

Givens

`A=140 \pi \ cm^(2) \\r=20 \cm`

The area of a circular sector is defined as

`A=(\pi r^(2) \theta )/(360\°)`

Replacing given values, and solving for
`\theta`

`140 \pi =(\pi 20^(2) \theta )/(360\°)\\ 400 \theta = 50,400\\\theta = (50,400)/(400) \approx 126 \°`

Therefore, the central angle of the sector is 126°.