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In a convex n-gon, the sum of n - 1 internal angles is 1485 degrees.  What is n?

 Jun 26, 2020
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The total number of degrees in all the interior angles of an n-gon is  (n - 2)180o.

 

10 sides would be too few because they would create (10 - 2)180o  =  1440o; but this is close.

 

11 sides create (11 - 2)180o  =  1620o. Subtracting 1485o from this number gives 135o;

so if 10 of the angles give a total of 1485o and the 11th angle has 135o, we would get an 11-sided polygon.

 Jun 26, 2020

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