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

    16 · 2 · 180° · Polygon interior angle sums

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

    3 · 2 · 180° · Polygon interior angle sums

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

    10 · 2 · 180° · Polygon interior angle sums

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

    17 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 18-sided polygon using (n − 2) × 180°.

    18 · 2 · 180° · Polygon interior angle sums

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

    19 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    25 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    24 · 2 · 180° · Polygon interior angle sums

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

    7 · 2 · 180° · Polygon interior angle sums

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

    13 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104734 · 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 16-sided polygon using (n − 2) × 180°.

    2520°

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

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. Calculate the sum of the interior angles of a 18-sided polygon using (n − 2) × 180°.

    2880°

    Substitute n = 18: (18 − 2) × 180° = 16 × 180° = 2880°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    4140°

    Substitute n = 25: (25 − 2) × 180° = 23 × 180° = 4140°.

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

    1260°

    Substitute n = 9: (9 − 2) × 180° = 7 × 180° = 1260°.

  10. 10. 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°.

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

    900°

    Substitute n = 7: (7 − 2) × 180° = 5 × 180° = 900°.

  12. 12. 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 questions · Seed 104734 · 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 16-sided polygon using (n − 2) × 180°.

    16 · 2 · 180° · Polygon interior angle sums

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

    3 · 2 · 180° · Polygon interior angle sums

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

    10 · 2 · 180° · Polygon interior angle sums

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

    17 · 2 · 180° · Polygon interior angle sums

  5. 5. Calculate the sum of the interior angles of a 18-sided polygon using (n − 2) × 180°.

    18 · 2 · 180° · Polygon interior angle sums

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

    19 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

  8. 8. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    25 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    24 · 2 · 180° · Polygon interior angle sums

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

    7 · 2 · 180° · Polygon interior angle sums

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

    13 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104734 · 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 16-sided polygon using (n − 2) × 180°.

    2520°

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

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. Calculate the sum of the interior angles of a 18-sided polygon using (n − 2) × 180°.

    2880°

    Substitute n = 18: (18 − 2) × 180° = 16 × 180° = 2880°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. Calculate the sum of the interior angles of a 25-sided polygon using (n − 2) × 180°.

    4140°

    Substitute n = 25: (25 − 2) × 180° = 23 × 180° = 4140°.

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

    1260°

    Substitute n = 9: (9 − 2) × 180° = 7 × 180° = 1260°.

  10. 10. 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°.

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

    900°

    Substitute n = 7: (7 − 2) × 180° = 5 × 180° = 900°.

  12. 12. 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 questions · Seed 104734 · Age guidance, not curriculum certification