Polygon Angles

Ever wondered why stop signs have that specific octagonal shape? Understanding polygon angles helps explain how these everyday shapes work mathematically.

A polygon is simply a 2D shape made of straight sides, like triangles, squares, or pentagons. When all sides and angles are equal, it's called a regular polygon - think of a perfect hexagon in a honeycomb.

Here's the brilliant bit: interior angles (the angles inside the shape) follow a simple formula. For any polygon, the sum of interior angles equals $number of sides - 2$ × 180°. So a triangle's angles add up to 180°, whilst a square's add up to 360°.

Exterior angles are even simpler - they always add up to 360° for any polygon. For regular polygons, each exterior angle equals 360° ÷ number of sides. Remember that at each corner, the interior and exterior angles always add up to 180°.

Quick Check: A regular hexagon has exterior angles of 60° each (360° ÷ 6), so each interior angle must be 120° (180° - 60°).

The examples show two methods for finding angles - use whichever feels more natural to you. Practice with different polygons and you'll spot the patterns quickly!