Understanding Angles in Polygons

Interior and Exterior Angles in Polygons

Interior angles are the angles inside a polygon, and there's a brilliant pattern you can use to find their sum. A triangle's angles always add up to 180°, whilst a quadrilateral's angles total 360°. Keep going and you'll find a pentagon reaches 540°, and a hexagon hits 720°.

The magic formula is $n-2$ × 180°, where n equals the number of sides. This works for any polygon - just subtract 2 from the number of sides and multiply by 180°. It's that simple!

Exterior angles are formed when you extend one side of the polygon outward. Here's the brilliant bit: exterior and interior angles at the same vertex always add up to 180° (they're supplementary). Even more amazingly, all exterior angles of any polygon always add up to exactly 360° - no matter how many sides it has.

Quick Check: If you know an interior angle is 120°, the exterior angle must be 60° (since 120° + 60° = 180°).