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

The formula for calculating the sum of the interior angles of a polygon with n sides is derived from the relationship that the sum is equal to 180 degrees multiplied by the number of triangles that can be formed within that polygon.

For any polygon, you can divide it into (n - 2) triangles by drawing diagonals from one vertex to all other non-adjacent vertices. Each triangle has interior angles that sum up to 180 degrees. Therefore, when you multiply the number of triangles, (n - 2), by the sum of the angles in each triangle (180 degrees), you arrive at the formula for the sum of the interior angles:

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

This understanding is crucial for solving geometry problems involving polygons, as it not only helps in finding the total sum but also in deducing various properties related to the angles and sides of the polygon.

The other provided choices do not correctly represent the sum of the interior angles for polygons. For instance, 180n incorrectly suggests that the angles are just a linear function of the sides without accounting for the geometric configuration of triangles. Meanwhile, 360 does not scale with the number of sides n and only represents the sum of angles in a