SOLUTION: what is the number of sides a polygon has if the sum of the degree measures of the interior angle is 180°?

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Question 247321: what is the number of sides a polygon has if the sum of the degree measures of the interior angle is 180°?
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
what is the number of sides a polygon has if the sum of the degree measures of the interior angle is 180°?

The formula for the S, the sum of the degree measures of the interior
angles of a polygon with n sides is 

S=%28n-2%29%2A%22180%B0%22

So we substitute %22180%B0%22 for S

%22180%B0%22=%28n-2%29%2A%22180%B0%22 

Divide both sides by 180%B0

%22180%B0%22%2F%22180%B0%22=%28n-2%29%2A%22180%B0%22%2F%22180%B0%22

1=n-2

3=n

So the answer is:  It has 3 sides.

That means the polygon is a triangle.  

I'll bet you've known all along that the 

measures of the interior angles of a triangle

is 180°, now haven't you?  Maybe you didn't

know that a triangle was a polygon, but it is!

It's a polygon with three sides!

Edwin

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!



The sum of the interior angles of an -sided polygon is given by the formula:



So set the formula equal to your given sum and then solve for



John