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

Answer:

The central angle of the sector is 126°.

Step-by-step explanation:

Givens

$A=140 \pi \ cm^{2} \\r=20 \cm$

The area of a circular sector is defined as

$A=\frac{\pi r^{2} \theta }{360\°}$

Replacing given values, and solving for $\theta$

$140 \pi =\frac{\pi 20^{2} \theta }{360\°}\\ 400 \theta = 50,400\\\theta = \frac{50,400}{400} \approx 126 \°$

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

Answer 2

Answer:

I got it right. 108

Step-by-step explanation: