The interior angles of a polygon are in an arithmetic progression (A.P.).
The smallest angle is 120 degrees.
The common difference is 5 degrees.


The number of sides in the polygon.


Let's assume the number of sides in the polygon is n.


The sum of interior angles of a polygon with n sides is given by the formula:
Sum = (n-2) * 180 degrees


Given that the smallest angle is 120 degrees, we can use the formula to find the common difference.
120 = a + (n-1)d
120 = 120 + (n-1)5
0 = (n-1)5
n - 1 = 0
n = 1

So, the common difference is 5 degrees.


Using the formula, we can find the sum of interior angles of the polygon.
Sum = (n-2) * 180
Sum = (n-2) * 180
Sum = (1-2) * 180
Sum = -180

Since the sum of interior angles cannot be negative, we can conclude that n-2 = 0, which means n = 2.


From Step 2, we found that n = 2, which means there are only 2 sides. However, a polygon must have at least 3 sides. Therefore, this is not a valid solution.


Since the previous assumption was incorrect, let's assume the number of sides is n+1.

Using the formula, we can find the sum of interior angles of the polygon.
Sum = (n+1-2) * 180
Sum = n * 180

Since the interior angles are in an arithmetic progression, the sum of the angles can also be expressed as:
Sum = n/2 * (2a + (n-1)d)
n * 180 = n/2 * (2 * 120 + (n-1) * 5)

Simplifying the equation:
2 * 180 = 120 + 5n - 5
360 = 120 + 5n - 5
360 = 115 + 5n
245 = 5n
n = 49

Therefore, the number of sides in the polygon is 49+1 = 50.


Using the formula for the sum of interior angles, we can verify the answer:
Sum = (n-2) * 180
Sum = (50-2) * 180
Sum = 48 * 180
Sum = 8640

Since the sum of interior angles of a polygon with 50 sides is 8640 degrees, this confirms that the answer is correct.


The number of sides in the polygon is 50, which means option '9' is incorrect.

Sum of the interior angles of a polygon is = (2n - 4)*π/2