Polygon Interior Angles Explorer

About This MicroSim

This interactive visualization demonstrates how the sum of interior angles in a polygon relates to the number of sides through triangulation.

Key Formulas

Interior Angle Sum

For a polygon with \(n\) sides:

\[S = (n - 2) \times 180°\]

Each Interior Angle (Regular Polygon)

For a regular polygon with \(n\) sides:

\[I = \frac{(n - 2) \times 180°}{n}\]

Exterior Angle (Regular Polygon)

\[e = \frac{360°}{n}\]

How Triangulation Works

Any polygon can be divided into triangles by drawing diagonals from one vertex. A polygon with \(n\) sides can be divided into \((n-2)\) triangles. Since each triangle has angles summing to 180°, the polygon's interior angles sum to \((n-2) \times 180°\).

Interactions

Slider: Change the number of sides (3-12)
Show Triangulation: Toggle diagonal lines showing triangle divisions
Show Angles: Toggle angle arc indicators

Learning Objectives

Apply the interior angle sum formula
Understand why the formula works through triangulation
Calculate individual angles in regular polygons

Bloom's Taxonomy Level

Applying and Understanding