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Updated Mar 18, 2026

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Understanding Angles in Polygons

Lucy

@lucy_xo

Ever wondered why triangles always have angles that add up... Show more

ANGLES IN POLYGONS: Interior

3 sides, angies in a triangle add up to
$A$3 sides.

4 sides, angies in a quadrilactural
add upto 360°.

5 sid

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° $since 120° + 60° = 180°$ .

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Updated Mar 18, 2026

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1 page

Understanding Angles in Polygons

Lucy

@lucy_xo

Ever wondered why triangles always have angles that add up to 180°, or how architects calculate angles in complex shapes? Understanding angles in polygons is like having a mathematical superpower that helps you solve puzzles involving any shape with straight... Show more

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Interior and Exterior Angles in Polygons

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!

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