The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Then the number of its sides is

Sum of the interior angles of a polygon is given by (2n-4)90

Smallest interior angle = 120

Let the number of sides of the convex-polygon be n 

$$\frac{n}{2}\left(2(120)+\left(n-1\right)\times\ 5\right)=(2n-4)90$$

n(240+5n-5)=360n-720

$$5n^2+235n=360n-720$$

$$5n^2-125n+720=0$$

$$n^2-25n+144=0$$

n=9,16

for a polygon to be convex, each interior angle should be less than 180

The interior angle when n=16 is 120+15*5=195 So n is not equal to 16

Interior angle when n =9 is 120+8*5 =160 

No of sides of the polygon =9

B is the correct answer.