Polygons
The interior angle of an gon is more than the interior angle of a gon.
What is ?
The answer is 6.
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1 solution
For n-gon,, Sum of angles is (n-2)(180). For 2n-gon, Sum of angles is (2n-2)(180). For each angle in n-gon: ((n-2)(180)/n). For each angle in 2n-gon:((2n-2)(180)/2n). Since int angle of 2n-gon is 30 degrees more than int angle of n-gon, ((n-2)(180)/n) + 30 = ((2n-2)(180)/2n) 2(n-2)(180) + 30(2n) = (2n-2)(180) 360n - 720 + 60n = 360n - 360 60n = 360 => n = 6.