Wednesday, 19 October 2011

Progressions - 2 (IIFT-2008)

The interior angles of a polygon are in A.P. If the smallest angle is 1200 and common difference is 50, then the number of sides in the polygon is:
(A) 7    (B) 8    (C) 9    (D)None of the above
Solution follows here:

Solution:

Given that smallest interior angle = 1200 and common difference 50

∴the series of interior angles is 1200, 1250, 1300,….

Exterior angle = 1800 – Interior angle

∴the series of corresponding exterior angles is 600,550,500,…

This is a decreasing Arithmetic Progression with

initial term ‘a’ = 60;           common difference ‘d’ = -5;

Let the polygon has ‘n’ sides.

Sum of n terms of AP  = n(2a+(n-1)d)/2                     ----- >(1)

Sum of exterior angles of any polygon = 3600        ----- >(2)
From (1) and (2),
360     = n(2a+(n-1)d)/2
360     = n(120+(n-1)(-5))/2
360     = n(125-5n)/2
720     = 5n(25-n)
144     = n(25-n)
Instead of solving the equation, we go for checking multiple choice options one by one:
Put n = 7, 144 = 7(18)      wrong
Put n = 8, 144 = 8(17)      wrong
Put n = 9, 144 = 9(16)      correct