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MathsAges 13-15

Polygon interior angle sums

Use (n − 2) × 180° to calculate the sum of interior angles of an n-sided polygon. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Polygon interior angle sums

Take your time. Show your thinking.

  1. 1. Calculate the sum of the interior angles of a 23-sided polygon using (n − 2) × 180°.

    23 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 6-sided polygon using (n − 2) × 180°.

    6 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    26 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    11 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    5 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    27 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    17 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 29-sided polygon using (n − 2) × 180°.

    29 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  10. 10. Calculate the sum of the interior angles of a 19-sided polygon using (n − 2) × 180°.

    19 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 13-sided polygon using (n − 2) × 180°.

    13 · 2 · 180° · Polygon interior angle sums

  12. 12. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    3 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 45 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. Calculate the sum of the interior angles of a 23-sided polygon using (n − 2) × 180°.

    3780°

    Substitute n = 23: (23 − 2) × 180° = 21 × 180° = 3780°.

  2. 2. Calculate the sum of the interior angles of a 6-sided polygon using (n − 2) × 180°.

    720°

    Substitute n = 6: (6 − 2) × 180° = 4 × 180° = 720°.

  3. 3. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    4320°

    Substitute n = 26: (26 − 2) × 180° = 24 × 180° = 4320°.

  4. 4. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    1620°

    Substitute n = 11: (11 − 2) × 180° = 9 × 180° = 1620°.

  5. 5. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    540°

    Substitute n = 5: (5 − 2) × 180° = 3 × 180° = 540°.

  6. 6. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    4500°

    Substitute n = 27: (27 − 2) × 180° = 25 × 180° = 4500°.

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    2700°

    Substitute n = 17: (17 − 2) × 180° = 15 × 180° = 2700°.

  8. 8. Calculate the sum of the interior angles of a 29-sided polygon using (n − 2) × 180°.

    4860°

    Substitute n = 29: (29 − 2) × 180° = 27 × 180° = 4860°.

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    3240°

    Substitute n = 20: (20 − 2) × 180° = 18 × 180° = 3240°.

  10. 10. Calculate the sum of the interior angles of a 19-sided polygon using (n − 2) × 180°.

    3060°

    Substitute n = 19: (19 − 2) × 180° = 17 × 180° = 3060°.

  11. 11. Calculate the sum of the interior angles of a 13-sided polygon using (n − 2) × 180°.

    1980°

    Substitute n = 13: (13 − 2) × 180° = 11 × 180° = 1980°.

  12. 12. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    180°

    Substitute n = 3: (3 − 2) × 180° = 1 × 180° = 180°.

12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Polygon interior angle sums

Take your time. Show your thinking.

  1. 1. Calculate the sum of the interior angles of a 23-sided polygon using (n − 2) × 180°.

    23 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 6-sided polygon using (n − 2) × 180°.

    6 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    26 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    11 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    5 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    27 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    17 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 29-sided polygon using (n − 2) × 180°.

    29 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  10. 10. Calculate the sum of the interior angles of a 19-sided polygon using (n − 2) × 180°.

    19 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 13-sided polygon using (n − 2) × 180°.

    13 · 2 · 180° · Polygon interior angle sums

  12. 12. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    3 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. Calculate the sum of the interior angles of a 23-sided polygon using (n − 2) × 180°.

    3780°

    Substitute n = 23: (23 − 2) × 180° = 21 × 180° = 3780°.

  2. 2. Calculate the sum of the interior angles of a 6-sided polygon using (n − 2) × 180°.

    720°

    Substitute n = 6: (6 − 2) × 180° = 4 × 180° = 720°.

  3. 3. Calculate the sum of the interior angles of a 26-sided polygon using (n − 2) × 180°.

    4320°

    Substitute n = 26: (26 − 2) × 180° = 24 × 180° = 4320°.

  4. 4. Calculate the sum of the interior angles of a 11-sided polygon using (n − 2) × 180°.

    1620°

    Substitute n = 11: (11 − 2) × 180° = 9 × 180° = 1620°.

  5. 5. Calculate the sum of the interior angles of a 5-sided polygon using (n − 2) × 180°.

    540°

    Substitute n = 5: (5 − 2) × 180° = 3 × 180° = 540°.

  6. 6. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    4500°

    Substitute n = 27: (27 − 2) × 180° = 25 × 180° = 4500°.

  7. 7. Calculate the sum of the interior angles of a 17-sided polygon using (n − 2) × 180°.

    2700°

    Substitute n = 17: (17 − 2) × 180° = 15 × 180° = 2700°.

  8. 8. Calculate the sum of the interior angles of a 29-sided polygon using (n − 2) × 180°.

    4860°

    Substitute n = 29: (29 − 2) × 180° = 27 × 180° = 4860°.

  9. 9. Calculate the sum of the interior angles of a 20-sided polygon using (n − 2) × 180°.

    3240°

    Substitute n = 20: (20 − 2) × 180° = 18 × 180° = 3240°.

  10. 10. Calculate the sum of the interior angles of a 19-sided polygon using (n − 2) × 180°.

    3060°

    Substitute n = 19: (19 − 2) × 180° = 17 × 180° = 3060°.

  11. 11. Calculate the sum of the interior angles of a 13-sided polygon using (n − 2) × 180°.

    1980°

    Substitute n = 13: (13 − 2) × 180° = 11 × 180° = 1980°.

  12. 12. Calculate the sum of the interior angles of a 3-sided polygon using (n − 2) × 180°.

    180°

    Substitute n = 3: (3 − 2) × 180° = 1 × 180° = 180°.

12 questions · Seed 45 · Age guidance, not curriculum certification