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(n − 2) × 180°

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°.

📐 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°