GEO013 · Geometry basics · Classes 7–10
Polygon angle sums
A polygon with n sides can be split into n − 2 triangles from one vertex, so its interior angles add to (n − 2) × 180°.
(n − 2) × 180°Polygon angle sums
📐 Formula
angle sum = (n − 2) × 180°
✏️ Worked example
A heptagon (n = 7): (7 − 2) × 180° = 900°.
🌍 Where it is used
Designing tiles, frames and roof shapes.
❓ Quick check
Angle sum of a hexagon?
🏋️ Practice
EasyAngle sum of a pentagon?
Answer: 540°
MediumA polygon's angles add to 1440°. How many sides?
Answer: 10
ChallengeAngle sum of a quadrilateral?
Answer: 360°