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

    10 · 2 · 180° · Polygon interior angle sums

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

    29 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 28-sided polygon using (n − 2) × 180°.

    28 · 2 · 180° · Polygon interior angle sums

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

    18 · 2 · 180° · Polygon interior angle sums

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

    16 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 14-sided polygon using (n − 2) × 180°.

    14 · 2 · 180° · Polygon interior angle sums

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

    3 · 2 · 180° · Polygon interior angle sums

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

    5 · 2 · 180° · Polygon interior angle sums

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

    21 · 2 · 180° · Polygon interior angle sums

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

    6 · 2 · 180° · Polygon interior angle sums

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

    4 · 2 · 180° · Polygon interior angle sums

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

    8 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 46 · 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 10-sided polygon using (n − 2) × 180°.

    1440°

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

  2. 2. 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°.

  3. 3. Calculate the sum of the interior angles of a 28-sided polygon using (n − 2) × 180°.

    4680°

    Substitute n = 28: (28 − 2) × 180° = 26 × 180° = 4680°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. Calculate the sum of the interior angles of a 14-sided polygon using (n − 2) × 180°.

    2160°

    Substitute n = 14: (14 − 2) × 180° = 12 × 180° = 2160°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

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

    360°

    Substitute n = 4: (4 − 2) × 180° = 2 × 180° = 360°.

  12. 12. 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°.

12 questions · Seed 46 · 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 10-sided polygon using (n − 2) × 180°.

    10 · 2 · 180° · Polygon interior angle sums

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

    29 · 2 · 180° · Polygon interior angle sums

  3. 3. Calculate the sum of the interior angles of a 28-sided polygon using (n − 2) × 180°.

    28 · 2 · 180° · Polygon interior angle sums

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

    18 · 2 · 180° · Polygon interior angle sums

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

    16 · 2 · 180° · Polygon interior angle sums

  6. 6. Calculate the sum of the interior angles of a 14-sided polygon using (n − 2) × 180°.

    14 · 2 · 180° · Polygon interior angle sums

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

    3 · 2 · 180° · Polygon interior angle sums

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

    5 · 2 · 180° · Polygon interior angle sums

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

    21 · 2 · 180° · Polygon interior angle sums

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

    6 · 2 · 180° · Polygon interior angle sums

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

    4 · 2 · 180° · Polygon interior angle sums

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

    8 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 46 · 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 10-sided polygon using (n − 2) × 180°.

    1440°

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

  2. 2. 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°.

  3. 3. Calculate the sum of the interior angles of a 28-sided polygon using (n − 2) × 180°.

    4680°

    Substitute n = 28: (28 − 2) × 180° = 26 × 180° = 4680°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. Calculate the sum of the interior angles of a 14-sided polygon using (n − 2) × 180°.

    2160°

    Substitute n = 14: (14 − 2) × 180° = 12 × 180° = 2160°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

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

    360°

    Substitute n = 4: (4 − 2) × 180° = 2 × 180° = 360°.

  12. 12. 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°.

12 questions · Seed 46 · Age guidance, not curriculum certification