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 angleSince we are subtracting the interior angles from a constant, the exterior angles will also be in an APThe 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 $0.5 \cdot n \cdot (2a + (n-1)d)$, where 'a' is the starting term and 'd' is the commondifference.$0.5 \cdot n \cdot (2 \cdot 60^{\circ} + (n-1) \cdot (-5^{\circ})) = 360^{\circ}$$120 - 5n^{2} + 5n = 720$$5n^{2} - 125n + 720 = 0$$n^{2} - 25n + 144 = 0$$(n-9)(n-16)=0$Therefore, can be 9 or 16.If the number of sides is 16, then the largest external angle will be $60 - 15 \cdot 5 = -15^{\circ}$. Therefore, we can eliminate this case.The number of sides in the polygon must be 9. Therefore, option C is the right answer.