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

Guest Jun 26, 2020

#1**0 **

The total number of degrees in all the interior angles of an n-gon is (n - 2)180^{o}.

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

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

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

geno3141 Jun 26, 2020