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Question

An exterior angle of a regular polygon having n-sides is more than that of the polygon having n2 sides by 50, then the number of the sides of each polygon are 6 and 38.

State true or false.

A
True
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B
False
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Solution

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=360n
Hence according to the given conditions,
360n=360n2+50360n=(50n2+360)5n236n+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±b24ac2an=36±(36)24(5)(36)2(5)n=36±129672010n=36±57610n=36±2410
or n=36+2410,362410n=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

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