Interior Angle of Polygon
Launch this tool in a distraction-free environment optimized for classroom instruction.
About
What is the Polygon Angle Sum Simulator?
The Polygon Angle Sum Simulator is a beautiful, interactive visual proof environment. It allows students to
explore the fundamental geometric principle that the sum of interior angles in any n-sided polygon
is always (n - 2) × 180°. By animating the deconstruction of custom-shaped polygons, the
abstract formula becomes a concrete, unforgettable visual experience.
Mathematical Applications
This simulator unpacks the hidden logic inside everyday shapes, proving theorems through direct manipulation
and animation.
Triangulation of Polygons
Why the (n - 2) in the formula? The animation clearly demonstrates that by drawing
non-intersecting diagonals from a single vertex, any polygon can be perfectly split into exactly two
fewer triangles than it has sides.
The 180° Rule (Half-Circles)
Once the polygon is split into triangles, the simulator extracts the three interior angles of every
triangle. As they slide to the right and align on a flat baseline, students instantly see that each
triangle's angles form a perfect half-circle (180°), proving that the total interior angle sum is
just the number of triangles multiplied by 180°.