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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 8-sided polygon using (n − 2) × 180°.

    8 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 21-sided polygon using (n − 2) × 180°.

    21 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 30-sided polygon using (n − 2) × 180°.

    30 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    22 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums

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

    10 · 2 · 180° · Polygon interior angle sums

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

    27 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums

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

    29 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 16-sided polygon using (n − 2) × 180°.

    16 · 2 · 180° · Polygon interior angle sums

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

    11 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 53 · 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 8-sided polygon using (n − 2) × 180°.

    1080°

    Substitute n = 8: (8 − 2) × 180° = 6 × 180° = 1080°.

  2. 2. Calculate the sum of the interior angles of a 21-sided polygon using (n − 2) × 180°.

    3420°

    Substitute n = 21: (21 − 2) × 180° = 19 × 180° = 3420°.

  3. 3. 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°.

  4. 4. Calculate the sum of the interior angles of a 30-sided polygon using (n − 2) × 180°.

    5040°

    Substitute n = 30: (30 − 2) × 180° = 28 × 180° = 5040°.

  5. 5. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    3600°

    Substitute n = 22: (22 − 2) × 180° = 20 × 180° = 3600°.

  6. 6. 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°.

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

    1440°

    Substitute n = 10: (10 − 2) × 180° = 8 × 180° = 1440°.

  8. 8. 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°.

  9. 9. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    3960°

    Substitute n = 24: (24 − 2) × 180° = 22 × 180° = 3960°.

  10. 10. 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°.

  11. 11. Calculate the sum of the interior angles of a 16-sided polygon using (n − 2) × 180°.

    2520°

    Substitute n = 16: (16 − 2) × 180° = 14 × 180° = 2520°.

  12. 12. 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°.

12 questions · Seed 53 · 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 8-sided polygon using (n − 2) × 180°.

    8 · 2 · 180° · Polygon interior angle sums

  2. 2. Calculate the sum of the interior angles of a 21-sided polygon using (n − 2) × 180°.

    21 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 30-sided polygon using (n − 2) × 180°.

    30 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    22 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums

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

    10 · 2 · 180° · Polygon interior angle sums

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

    27 · 2 · 180° · Polygon interior angle sums

  9. 9. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums

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

    29 · 2 · 180° · Polygon interior angle sums

  11. 11. Calculate the sum of the interior angles of a 16-sided polygon using (n − 2) × 180°.

    16 · 2 · 180° · Polygon interior angle sums

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

    11 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 53 · 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 8-sided polygon using (n − 2) × 180°.

    1080°

    Substitute n = 8: (8 − 2) × 180° = 6 × 180° = 1080°.

  2. 2. Calculate the sum of the interior angles of a 21-sided polygon using (n − 2) × 180°.

    3420°

    Substitute n = 21: (21 − 2) × 180° = 19 × 180° = 3420°.

  3. 3. 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°.

  4. 4. Calculate the sum of the interior angles of a 30-sided polygon using (n − 2) × 180°.

    5040°

    Substitute n = 30: (30 − 2) × 180° = 28 × 180° = 5040°.

  5. 5. Calculate the sum of the interior angles of a 22-sided polygon using (n − 2) × 180°.

    3600°

    Substitute n = 22: (22 − 2) × 180° = 20 × 180° = 3600°.

  6. 6. 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°.

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

    1440°

    Substitute n = 10: (10 − 2) × 180° = 8 × 180° = 1440°.

  8. 8. 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°.

  9. 9. Calculate the sum of the interior angles of a 24-sided polygon using (n − 2) × 180°.

    3960°

    Substitute n = 24: (24 − 2) × 180° = 22 × 180° = 3960°.

  10. 10. 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°.

  11. 11. Calculate the sum of the interior angles of a 16-sided polygon using (n − 2) × 180°.

    2520°

    Substitute n = 16: (16 − 2) × 180° = 14 × 180° = 2520°.

  12. 12. 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°.

12 questions · Seed 53 · Age guidance, not curriculum certification