SOLUTION: How many sides does a polygon have if the sum of its angle measures is 2700 degrees and how do you find this?

Question 262831: How many sides does a polygon have if the sum of its angle measures is 2700 degrees and how do you find this?
Found 2 solutions by drk, Theo:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
We need the following formula:

where D = total degrees, and n = number of sides.
fro above we have

step 1 - divide by 180 to get

step 2 - add 2 to get

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sum of the interior angles is 2700 degrees.

the sum of the interior angles of a polygon is given by the equation:

s = (n-2)*180 where:

s = the sum of the interior angles.
n = the number of sides of the polygon.

given that s = 2700, this equation becomes:

2700 = (n-2)*180

simplify to get:

2700 = 180*n - 360

add 360 to both sides of this equation to get:

3060 = 180*n

divide both sides of this equation by 180 to get:

n = 3060/180 = 17

the polygon has 17 sides.

each interior angle of this polygon = 2700/17 = 158.8235294

each exterior angle of this polygon = 180 - 158.8235294 = 21.17647059

17 * 21.17647059 = 360 degrees which is should since the sum of the exterior angles of a polygon is always 360 degrees.

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