The interior angles of a
polygon are in A.P. If the smallest angle is 120

^{0}and common difference is 5^{0}, 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 = 120

^{0}and common difference 5^{0}
∴the series of interior angles
is 120

^{0}, 125^{0}, 130^{0},….
Exterior
angle = 180

^{0}– Interior angle
∴the series of corresponding
exterior angles is 60

^{0},55^{0},50^{0},…**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 = 360

^{0}----- >(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

**∴ Answer is (C)**
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