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Sir, could you kindly assist me solve this problem... Thank you in advance. Two regular polygons have sides m and n respectively. If the number of degrees in an angle of the first is equal to the number of grades in an angle of the second, show that, 20/n - 18/m = 1.

Sir, could you kindly assist me solve this problem... Thank you in advance.

 

Two regular polygons have sides m and n respectively. If the number of degrees in an angle of the first is equal to the number of grades in an angle of the second, show that,       

20/n - 18/m = 1.

Grade:11

1 Answers

Latika Leekha
askIITians Faculty 165 Points
5 years ago
Hello student,
The sum of interior angles of regular polygon having “m” sides = (2m – 4) right angles
So, this means that one angle of regular polygon of m sides = (2m-4)/m right angles.
In the similar fashion, one angle of regular polygon of n sides = (2n-4)/n right angles
So, by the condition given in the question, we have
[(2m-4)/m] X 90 = [(2n-4)/n] X 100
This gives 2 [(1-2/m)] . 90 = 2 [(1-2/n)] . 100
So, 9-18/m = 10-20/n
This gives 20/n – 18/m = 1.

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