What is the formula for the sum of interior angles of a convex polygon with n sides?

The formula for the sum of the interior angles of a convex polygon with n sides is derived from the concept that a polygon can be divided into triangles. For any polygon, you can draw diagonals from one vertex to the other non-adjacent vertices, effectively creating triangles within the polygon.

To understand the formula, consider that an n-sided polygon can be divided into (n-2) triangles, because you can create (n-2) triangles by drawing diagonals from one vertex. Each triangle has interior angles that sum up to 180 degrees. Therefore, the total sum of the interior angles of the polygon can be calculated by multiplying the number of triangles (n-2) by the sum of angles in each triangle (180 degrees).

This leads to the formula:

Sum of interior angles = 180(n - 2).

This formula is essential for solving problems related to polygons in geometry, helping in the understanding of angles in which polygon shapes can be formed. The other choices do not accurately reflect this relationship and thus are not considered valid for the sum of interior angles in polygons.