Question

the difference between the interior angle of regular polygon of (n+1)sides and an interior angle of regular polygon of n sides is 4degree find the value of n

Answer 1

Fact: The sum of the exterior angles is 360 degrees.
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n-1 sided Polygon DATA
Size of each exterior angle = 360/(n-1)
Size of each interior angle = 180-[360/(n-1)]
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n+1 sided Polygon DATA
Size of each exterior angle = 360/(n+1)
Size of each interior angle = 180-[360/(n+1)]
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Equation: Difference = 4 degrees
180-[360/(n+1)] - [180-[360/(n-1)] = 4 degrees
(360/(n+1) + 360/(n-1) = 4 degrees
1/(n+1) + 1/(n-1) = 1/90
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90(n-1)+90(n+1) = (n+1)(n-1)