The interior angles of a polygon are in Arithmetic Progression. If the smallest angle is 120° and common difference is 5°, then number of sides in the polygon is:

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*n*(2a + (n-1)d), where 'a' is the starting term and 'd' is the common difference.
0.5*n*(2*60° + (n-1)*(-5°)) = 360°
120$$n$$ - 5$$n^2$$ + 5$$n$$ = 720
5$$n^2$$ - 125$$n$$ + 720 = 0
$$n^2$$ - 25$$n$$ + 144 =0.
$$(n-9)(n-16) = 0$$

Therefore, $$n$$ 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.