How to find the number of sides of a polygon based off of the sum of its interior polygons.

Question

The sum of all the interior angles of seven polygons is (180)(17). Find the total number of sides of the polygon.

Answer 1

The formula for sum of interior angles of a polygon is s = (n-2) * 180 where s represents the sum of the interior angles and n represent the number of sides of the polygon. If we have the sum then we need to solve for n by following the rules for solving equations.

For example: If the sum of interior angles 1,080 then we will that in for s.

1,080 = (n-2) * 180

To solve for n, we need to get rid of the 180 by divide both sides by 180 because the opposite of multiplication is division. 1,080/180 = 6 so now my equation is

6 = n - 2

To solve for n, we need to get rid of the -2 by adding 2 to both sides.

8 = n

Final Answer: If the sum of the interior angles of a polygon is 1,080 degrees then the polygon has 8 sides.