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
Algebra ->
Polygons
-> 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
Log On
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?
---
Fact: The sum of the exterior angles is 360 degrees.
-------------------------------------------------
n-1 sided Polygon DATA
Size of each exterior angle = 360/(n-1)
Size of each interior angle = 180-[360/(n-1)]
==========================================
n+1 sided Polygon DATA
Size of each exterior angle = 360/(n+1)
Size of each interior angle = 180-[360/(n+1)]
===========================================
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
----
-40(n-1)+40(n+1) = (n+1)(n-1)
80 = n^2-1
n^2 = 81
n = 9
================================
2)In a regular polygon the difference between the exterior angle of a (n-1) &(n+2) Sided polgon is 6 degree. Find n?
---
Comment: Same process
===========================
Cheers,
Stan H.
(