What is the formula for calculating the sum of interior angles in any polygon?

The formula for calculating the sum of interior angles in any polygon is given by (n-2) x 180, where n represents the number of sides of the polygon. This relationship arises from the fact that any polygon can be divided into triangles. Since the sum of the angles in a triangle is always 180 degrees, the number of triangles that can be formed within a polygon is equal to the number of sides minus two.

For example, if you take a triangle (which has 3 sides), the sum of its interior angles is (3-2) x 180 = 1 x 180 = 180 degrees. For a quadrilateral (4 sides), the calculation would be (4-2) x 180 = 2 x 180 = 360 degrees. Continuing this pattern, the formula reliably calculates the sum of interior angles for all polygons.

The other options presented do not correctly reflect the relationship between the number of sides and the sum of the angles based on triangulation. The second option (n x 180) would suggest that each angle equals 180 degrees, which is not the case for polygons with more than three sides. The third option (n+2) x 180 misinterprets the formula entirely