The correct option is
B False
Given: An exterior angle of a regular polygon having
n-sides is more than that of the polygon having
n2 sides by
50∘To find the number of the sides of each polygon are 6 and 38.
Solution:
We know in any polygon with n number of sides, the exterior angle, A=360∘n
Hence according to the given conditions,
360∘n=360∘n2+50∘⟹360∘n=(50∘n2+360∘)⟹5n2−36n+36=0
This is of the form ax2+bx+c=0 where a=5,b=−36,c=36, hence the roots of the equation will be
n=−b±√b2−4ac2a⟹n=36±√(36)2−4(5)(36)2(5)⟹n=36±√1296−72010⟹n=36±√57610⟹n=36±2410
or n=36+2410,36−2410⟹n=6,1.2
As the sides cannot be in decimal. So n=6
Hence the number of the sides of each polygon are n=6 and n2=36