SOLUTION: The difference between the exterior angles of two regular polygon having sides equal to n and n+1 is 12. Find the value of n

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Question 983192: The difference between the exterior angles of two regular polygon having sides equal to n and n+1 is 12. Find the value of n
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

An exterior angle of a n sided polygon is equal to 360%2Fn+ and that of %28n+%2B+1%29 sided polygon is 360%2F%28n+%2B+1%29+.
if the difference between the exterior angles of two regular polygon is 12, we have
360%2Fn+-+360%2F%28n+%2B+1%29+=12...........solve for n
%28360%28n+%2B+1%29%29%2F%28n%28n+%2B+1%29%29++-+360n%2F%28n%28n+%2B+1%29%29=12
%28360%28n+%2B+1%29++-+360n%29%2F%28n%28n+%2B+1%29%29=12
%28360n+%2B+360+-+360n%29=12n%28n+%2B+1%29
+360+=12n%28n+%2B+1%29
+360+%2F12=n%28n+%2B+1%29
+30=n%5E2+%2B+n
+0=n%5E2+%2B+n-30
+0=n%5E2+-5n%2B+6n-30
+0=%28n%5E2+-5n%29%2B+%286n-30%29
+0=n%28n+-5%29%2B+6%28n-5%29
+0+=+%28n-5%29+%28n%2B6%29
solutions:
if +0+=+%28n-5%29+=>n=5
if+0+=+%28n%2B6%29=>n=-6...=.> since n cannot be negative number, disregard solution n=-6
so, your solution is highlight%28n=5%29