The interior angles of a polygon are in A.P. The smallest anlge is `((2pi)/(3))^(c )` and common difference is `5^(@)`. Find the number of sides in the polygon.

Explanation

To solve the problem, we need to find the number of sides \( n \) of a polygon where the interior angles are in arithmetic progression (A.P.). The smallest angle is given as \( \frac{2\pi}{3} \) radians, and the common difference is \( 5^\circ \).

### Step-by-Step Solution:

1. **Understanding the Sum of Interior Angles**:
The sum of the interior angles of a polygon with \( n \) sides is given by the formula:
\[
S = (n - 2) \times 180^\circ
...