Does the formula

Sum of internal angles of a polygon = (n - 2)x180 degrees, where n represents number of sides,
work for polygons of interacting sides?

Does the formula

Sum of internal angles of a polygon = (n - 2)x180 degrees, where n represents number of sides,
work for polygons of intersecting sides?
correction please 'intersecting' in the place of 'interacting'

no, intersecting sides would create more than one polygon.

You would then calculate the sum for each of the individual polygons.

Thanks a lot for your help

The formula you mentioned, "Sum of internal angles of a polygon = (n - 2) x 180 degrees," applies to any polygon, including polygons with intersecting sides. This formula provides a direct relationship between the number of sides (n) of a polygon and the sum of its internal angles.

To understand why this formula works, we can break it down into two components:

1. (n - 2): This part of the formula represents the number of triangles that can be formed by drawing diagonals from a single vertex of the polygon. In any polygon, regardless of whether its sides are intersecting or not, it can always be divided into triangles in this way. For example, a quadrilateral (a polygon with four sides) can be divided into two triangles, a pentagon (five sides) can be divided into three triangles, and so on.

2. 180 degrees: This is the sum of the interior angles of a triangle. In a non-intersecting polygon, such as a rectangle or a regular hexagon, each interior angle is 180 degrees. Therefore, when we multiply the number of triangles (n - 2) by 180 degrees, we get the sum of all the internal angles of the polygon.

Hence, the formula holds true for any polygon, even those with intersecting sides, because the number of triangles formed by drawing diagonals from a single vertex remains the same, and the sum of the internal angles of each triangle is always 180 degrees.