The Math Meridian
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Angles in polygons

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Learn it Interior angle sum of an n-gon: $(n - 2) \times 180°$. Exterior angles always add to 360°, so each exterior angle of a regular n-gon is $360° \div n$.

Example: Find each interior angle of a regular octagon.

  1. Sum: $(8 - 2) \times 180 = 1{,}080°$.
  2. Each: $1{,}080 \div 8 = 135°$.
  3. Check: exterior $= 180 - 135 = 45 = 360 \div 8$ ✓.

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