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)   (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 , the sum of the degree measures of the interior
angles of a polygon with  sides is 



So we substitute  for 

 

Divide both sides by 







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)   (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
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