Iift 2008 Question 40
This is a detailed step-by-step solution for Iift 2008 Question 40. Understand the concept, common mistakes, and expert tips to solve similar questions in IIFT exam.
IIFT 2008
Explanation:
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 x n x (2a + (n-1)d), where 'a' is the starting term and 'd' is the common difference.
0.5 x n x (2 x 60° + (n-1) x (-5°)) = 360°
120 - 5 + 5 = 720
5 - 125 + 720 = 0
- 25 + 144 =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.