The interior angles of a polygon are in A.P. the smallest angle is `120^0` and the common difference is `5^0dot` Find the number of sides of the polygon.

Explanation

To find the number of sides of a polygon whose interior angles are in an arithmetic progression (A.P.), we can follow these steps:

### Step 1: Define the terms of the A.P.
The smallest angle of the polygon is given as \(120^\circ\), which is the first term \(a\) of the A.P. The common difference \(d\) is given as \(5^\circ\). Therefore, the interior angles can be expressed as:
- First angle: \(a = 120^\circ\)
- Second angle: \(a + d = 120^\circ + 5^\circ = 125^\circ\)
- Third angle: \(a + 2d = 120^\circ + 10^\circ = 130^\circ\)
- And so on, up to the \(n\)-th angle: \(a + (n-1)d = 120^\circ + (n-1) \cdot 5^\circ\)
...