6.1 Angles of Polygons

Triangle

3 sides. 1 Triangle. Sum of Interior Angle Measures is 180. Sum of Interior and Exterior angles is 540. Sum of all exterior angles is 360.

Quadrilateral

4 sides. 2 Triangles. Sum of Interior Angles is 360. Sum of all interior and exterior Angles is 720. Sum of all exterior Angles is 360.

Pentagon

5 sides. 3 Triangles. Sum of interior Angles is 540. Sum of all interior and exterior Angles is 900. Sum of all exterior Angles is 360.

Hexagon

6 sides. 4 Triangles. Sum of interior Angles is 720. Sum of all interior and exterior Angles is 1080. Sum of all exterior Angles is 360.

Polygon exterior Angles sum ( Theorem 6.2 )

For any convex polygon the sum of the exterior Angles is 360.

EXAMPLE for the N-Gon

Lets say the N stands for 12 in this case. 12 sides. 10 Triangles Sum of interior Angles is 1800. Sum of interior and exterior Angles is 2160 Sum of all exterior Angles is 360.

N-Gon

N sides. N - 2 Triangles. Sum of interior Angles is ( n - 2 ) • 180. Sum of interior and exterior Angles is n • 180. Sum of all exterior Angles is 360.

Polygon Interior Angles Sum ( Theorem 6.1 )

The sum of the interior Angles of a convex polygon with n-sides is ( n - 2 ) • 180.