What is polygon?
A polygon is a shape with three or more sides, in which each side touches another only at its endpoints. Some polygons that you are probably already familiar with are rectangles, squares, and triangles.
Sum of Interior Angles of a Regular Polygon
The sum of the interior angles of an n-sided regular polygon is n minus 2, times 1800 , where n represents a positive whole number.
Sum of interior angles of a polygon = 180(n-2)
Another way to remember the sum of the interior angles of a regular polygon is to cut the polygon into non-overlapping triangles by connecting vertices.
Knowing that sum of the interior angles of a triangle is 1800 , multiply the number of triangles by 1800 to get the sum of the interior angles of the polygon.
Example: Find the sum of the interior angles of a hexagon (6-sided polygon).
Again, the number of sides of a polygon is represented by n. In a hexagon, n = 6. Plug n into the formula:
180(n-2) =180(6-2) = 180.4 = 720
The sum of the interior angles of a hexagon is 7200