If the difference between an exterior angle of a regular polygon of n sides and an exterior angle of another - Maths - Rectilinear Figures

Question

If the difference between an exterior angle of a regular polygon of
n sides and an exterior angle of another regular polygon of n+1
sides is equal to 5?; find the value of n

Josepaul Paulachan · Accepted Answer

Dear Student The exterior angle of a n sided polygon = 3600nThe exterior angle of a n+1 sided polygon = 3600n+1given360n-360n+1=5360(n+1-n)n(n+1)=5360=5n(n+1)360=5n2+5n5n2+5n-360=0n2+n-72=0n2+9n-8n-72=0n(n+9)-8(n+9)=0(n-8)(n+9)=0n=8,-9n cannot have negative valuetherefore the value of n=8

If the difference between an exterior angle of a regular polygon of n sides and an exterior angle of another regular polygon of n+1 sides is equal to 5?; find the value of n