1some guys seem a big fan of IMO (this was for number "2011" :P)
Find the maximum number of sides of a n-sided polygon, the sum of all the angles of which is less than 2011° and hence find the sum of all the interior angles of the polygon.
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4 Answers
36nopes the polygon is not at all regular. Its dead easy. Just a lill formula work and Inequality kills the question.... :P
36I think i gotta post the solution..
The sum of all the angles of a n-sided polygon is given by 180° x (n - 2)
So, A To Q,
180° x (n - 2) ≤ 2011°
=> (n - 2) ≤ 11.17222....
but since, (n - 2) is a positive integer so,
(n - 2) = 11 [as we need to find the maximum number of sides]
=> n = 13
Thus, sum of all the interior angles = 180° x 11 = 1980° Ans...