Change the number of sides with the slider. Watch how many triangles the polygon splits into from one vertex, and see with your own eyes exactly why the interior angle sum formula is (n − 2) × 180°.
Why is a polygon's interior angle sum (n−2)×180°? The secret is splitting it into triangles. Draw diagonals from one vertex of a polygon to all the other vertices, and the shape splits into several triangles. For a pentagon, two diagonals create three triangles. Since one triangle's interior angles always sum to 180°, three triangles give 180×3=540° as the pentagon's interior angle sum. Every extra side adds one more triangle, which is exactly where the formula (number of sides−2)×180 comes from.
The reason honeycombs are stable in a hexagonal shape, and the ratio of pentagons to hexagons on a soccer ball, both come back to this same interior angle sum. Change the number of sides with the slider and see for yourself how many triangles it splits into, and how the interior angle sum changes.