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Year 7 · Shapes & Geometry

Angle sums of polygons

The angles inside a polygon add up to (sides − 2) × 180°. Exterior angles always add to 360°.

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How to do it

  1. Angle sum: (n − 2) × 180.
  2. Regular polygon: divide the sum by the number of angles.
  3. Missing angle: subtract the known angles from the sum.

Worked example

Angle sum of a hexagon
(6 − 2) × 180
720°

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A quadrilateral adds to 360°, a triangle to 180°.

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