SOLUTION: The measure of an interior angle of a regular polygon is 120. What is the number of sides for that polygon?

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Question 233725: The measure of an interior angle of a regular polygon is 120. What is the number of sides for that polygon?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles of a polygon is equal to:

(n-2) * 180

Each interior angle is equal to:

((n-2) * 180) / n

That means that:

120 = (n-2) * 180) / n

Multiply both sides by n to get:

120 * n = (n-2) * 180

Remove parentheses to get:

120 * n = 180 * n - 360

Subtract 120 * n from both sides and add 360 to both sides to get:

360 = 180 * n - 120 * n

Combine like terms to getr:

360 = 60 * n

Divide both sides by 60 to get:

6 = n

Number of sides of the polygon is 6 which makes it a hexagon.

Total degrees in a hexagon is (6-2) = 4 * 180 = 720

720 / 6 = 120 equals degree of each angle.

To colnfirm the formula is correct, take a polygon you know, like a triangle.

Each angle = 60
60 = (n-2) * 180 / n
60 * n = 180 * n - 360
120*n = 360
n = 3
formula is confirmed as correct.