For an n-sided polygon, how is the sum of interior angles determined?

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The sum of the interior angles of an n-sided polygon can be determined using the formula (n-2) * 180 degrees. This formula arises from the fact that a polygon can be divided into (n-2) triangles. Each triangle has a sum of interior angles equal to 180 degrees. Therefore, when you multiply the number of triangles, (n-2), by the 180 degrees per triangle, you get the total sum of the interior angles for the polygon.

For example, in a triangle (3-sided polygon), you have (3-2) * 180 = 1 * 180 = 180 degrees. In a quadrilateral (4-sided polygon), the calculation would be (4-2) * 180 = 2 * 180 = 360 degrees. This shows that as you increase the number of sides (n), the sum of the interior angles increases in a predictable manner based on this formula.

The other options do not correctly describe the relationship between the number of sides and the sum of the interior angles of a polygon. For instance, (n+2) does not relate to any geometric property of polygons, (2n) * 180 degrees would imply a relationship that's not applicable in this