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AP and polygon

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GMAT Score:720
by maihuna » Sun May 10, 2009 7:52 am
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120° , find the number of the sides of the polygon.


7
9
10
14
16
Charged up again to beat the beast :)
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by agoyal2 » Sun May 10, 2009 9:12 am
The external angles of the Polygon 60, 55, 54 etc and sum of external angles is 360:


So, As per AP:

[2a + (n-1)d]n/2 = S
[2*60 + (n-1)(-5)]n/2 = 360
120n-5n^2+5n=720
n^2-25n-144=0
n^2-9n-16n-144=0
n=9, 16

Not sure how to pick 9 or 16. Brute Force?? Is there a shorter method?
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