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) (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.
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