SOLUTION: 1)In a regular polygon the difference between the interior angle of a (n-1) sided polygon & (n+1) polygon is 9 degree. find n?
2)In a regular polygon the difference between the
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Question 342282: 1)In a regular polygon the difference between the interior angle of a (n-1) sided polygon & (n+1) polygon is 9 degree. find n?
2)In a regular polygon the difference between the exterior angle of a (n-1) &(n+2) Sided polgon is 6 degree. Find n?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1)In a regular polygon the difference between the interior angle of a (n-1) sided polygon & (n+1) polygon is 9 degree. find n?
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Fact: The sum of the exterior angles is 360 degrees.
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n-1 sided Polygon DATA
Size of each exterior angle = 360/(n-1)
Size of each interior angle = 180-[360/(n-1)]
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n+1 sided Polygon DATA
Size of each exterior angle = 360/(n+1)
Size of each interior angle = 180-[360/(n+1)]
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Equation: Difference = 9 degrees
180-[360/(n+1)] - [180-[360/(n-1)] = 9 degrees
-(360/(n+1) + 360/(n-1) = 9 degrees
-1/(n+1) + 1/(n-1) = 1/40
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-40(n-1)+40(n+1) = (n+1)(n-1)
80 = n^2-1
n^2 = 81
n = 9
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2)In a regular polygon the difference between the exterior angle of a (n-1) &(n+2) Sided polgon is 6 degree. Find n?
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Comment: Same process
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Cheers,
Stan H.
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