Indian Institute of Foreign Trade 2008 Solved Paper

It has been given that the interior angles in a polygon are in an arithmetic progression.
We know that the sum of all exterior angles of a polygon is 360°.
Exterior angle = 180° - interior angle
Since we are subtracting the interior angles from a constant, the exterior angles will also be in an AP
The starting term of the AP formed by the exterior angles will be 180°-120° = 60° and the common difference will be - 5°.
Let the number of sides in the polygon be 'n'.
=> The number of terms in the series will also be 'n'.
We know that the sum of an AP is equal to $0.5*\mathit{n}*\left(2\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}\right)$, where 'a' is the starting term and 'd' is the commondifference.
$0.5*\mathit{n}*\left(2*60°+\left(\mathit{n}-1\right)*\left(-5°\right)\right)=360°$
$120-5{\mathit{n}}^2+5\mathit{n}=720$
$5{\mathit{n}}^2-125\mathit{n}+720=0$
${\mathit{n}}^2-25\mathit{n}+144=0$
$\left(\mathit{n}-9\right)\left(\mathit{n}-16\right)=0$
Therefore, can be 9 or 16.
If the number of sides is 16, then the largest external angle will be $60-15*5=-15°$. Therefore, we can eliminate this case.
The number of sides in the polygon must be 9. Therefore, option C is the right answer.