Exploring a Formula for the Sum of Interior
Angles of an n-gon
Exploring quadrilaterals
Reflection Questions:
Explore each sketch to the left by moving the vertices around.
Check to see if the formula holds for all quadrilaterals, pentagons, and
hexagons.
In each case, explain why the formula seems to work. HINT: Click
on the "Show triangles" button.
Can the formula be generalized to any n-gon? If so, what would that
formula be? NOTE: Assume that one can locate a point P inside the
given n-gon such that all of the triangles are inside the polygon.
Develop a sketch in GSP to test the formula for a convex octagon.