sanju09 wrote:
Whereas I'm getting it as n^2 - 25 n + 144 = 0, hence two possibilities for n are 9 and 16, and both are there in the choices, fine. But if it mentions that 120º is the smallest angle, then are we sure that the 9th angle in the so called and described counterclockwise manner will be the greatest possibility for the formation of a convex polygon as demanded in the question. Or, did I need to mention "the greatest" before n in stem? Do I really need to edit my post, once?
What's the folly in the following piece of thought?
175º is the greatest possible interior angle in this fashion, such that 175 = 120 + 5 (n - 1) or n = [spoiler]12.[/spoiler]
[spoiler]D just IMO[/spoiler]
You are indeed right about the mistake I made in the calculation
Sum of interior angles of a convex polygon = (n-2)*180
Sum of the angles which are in AP = n/2(2*a+(n-1)*d) = n/2(2*120+ 5n-5) = n/2(5n+235)
since these two are equal
180n -360 = 5/2 (n^2+
47n)
72n - 144 = n^2+47n
n^2-25n-144 =0
(n-9)(n-16) =0
Still n cant be 16 because in that case ; the maximum angle will be more than 180 and it is mentioned that it is a convex polygon.
n=9
If indeed the number of sides were 12 as you suggested; the sum of all interior angles should be (n-2)*180 = 10*180 =1800
Now, the sum of AP = 6*(120+175) = 1770 and such a convex polygon cannot exist....
Hence D is not the option
Always borrow money from a pessimist, he doesn't expect to be paid back.
