Question

the difference between exterior angle of a reglar polygon of n sides and regular polygon of n+1 sides is 5 degree what are the number of sides of the polygon

Answer 1

Hey there,

             i) Since interior and exterior angles of a polygon are liner pair, if the difference in interior angles is 5 deg then difference in exterior angles is also 5 deg.

ii) An exterior angle of a n sided polygon = 360/n and that of (n + 1) sided polygon is 360/(n + 1)

iii) ==> 360/n - 360/(n + 1) = 5

Taking LCM, simplifying and rearranging, n² + n - 72 = 0
Factorizing, (n + 9)(n - 8) = 0

==> Either n = -9 or 8
But n being a counting number, it cannot be negative.

So n = 8

Hope this helps!