SOLUTION: The area of a circle is 804.2 square centimeters. The area of a sector of the circle is 268.1 square centimeters. What is the measure of the central angle that defines the secto

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Question 1187220: The area of a circle is 804.2 square centimeters.
The area of a sector of the circle is 268.1 square
centimeters. What is the measure of the central
angle that defines the sector?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the area of the circle is 804.2 square centimeters.
the area of the sector is 268.1 square centimeters.
the ratio of the area of the sector to the area of the circle is 268.1/804.2
multiply 360 degrees by that to get 120.0149217 degrees.

here's a reference.

https://www.storyofmathematics.com/area-of-sector

the part that i am referring to is when the angle is measured in degrees.
that formula is:

A = (θ/360)*π*r^2
A is the area of the sector.
pi*r^2 is the area of the circle.

since pi*r^2 is the area of the circle, and since the area of the circle is given as 804.2, the formula becomes:
A = (θ/360)*804.2
since the area of the swector is given as 268.1, the formula becomes:
268.1 = (theta/360) * 804.2
solve for (theta/360) to get:
theta/360 = 268.1/804.2 = .333747824.
multiply both sides of this equation by 360 to get:
theta = .333747824 * 360 = 120.0149217 degrees.

that's your solution.
120.0149217 degrees is the measure of the central angle of the sector.