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Mathematics · Grades 7–9

Interior angles of polygons

For a simple polygon, n is the number of sides and n ≥ 3.

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The key idea

For a simple polygon, n is the number of sides and n ≥ 3.

sum = (n − 2) × 180°

Worked examples

Find the interior-angle sum, in degrees, of a simple 29-sided polygon.

(29 − 2) × 180 = 4860

4860 °

Find the interior-angle sum, in degrees, of a simple 14-sided polygon.

(14 − 2) × 180 = 2160

2160 °

Try it yourself

  1. Find the interior-angle sum, in degrees, of a simple 24-sided polygon.

  2. Find the interior-angle sum, in degrees, of a simple 10-sided polygon.

Check your understanding

Answers and marking notes
  1. 3960 °

    (24 − 2) × 180 = 3960

  2. 1440 °

    (10 − 2) × 180 = 1440

Further reading and review references

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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.