<PRE><B>Question 233725</B>
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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