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

    12 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

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

    18 · 2 · 180° · Polygon interior angle sums

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

    14 · 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 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    15 · 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 10-sided polygon using (n − 2) × 180°.

    10 · 2 · 180° · Polygon interior angle sums

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

    25 · 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 4-sided polygon using (n − 2) × 180°.

    4 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104742 · 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 12-sided polygon using (n − 2) × 180°.

    1800°

    Substitute n = 12: (12 − 2) × 180° = 10 × 180° = 1800°.

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

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

    3240°

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

  7. 7. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    2340°

    Substitute n = 15: (15 − 2) × 180° = 13 × 180° = 2340°.

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

    1440°

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

  10. 10. 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°.

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

    360°

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

12 questions · Seed 104742 · 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 12-sided polygon using (n − 2) × 180°.

    12 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

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

    18 · 2 · 180° · Polygon interior angle sums

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

    14 · 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 20-sided polygon using (n − 2) × 180°.

    20 · 2 · 180° · Polygon interior angle sums

  7. 7. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    15 · 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 10-sided polygon using (n − 2) × 180°.

    10 · 2 · 180° · Polygon interior angle sums

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

    25 · 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 4-sided polygon using (n − 2) × 180°.

    4 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104742 · 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 12-sided polygon using (n − 2) × 180°.

    1800°

    Substitute n = 12: (12 − 2) × 180° = 10 × 180° = 1800°.

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

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

    3240°

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

  7. 7. Calculate the sum of the interior angles of a 15-sided polygon using (n − 2) × 180°.

    2340°

    Substitute n = 15: (15 − 2) × 180° = 13 × 180° = 2340°.

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

    1440°

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

  10. 10. 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°.

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

    360°

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

12 questions · Seed 104742 · Age guidance, not curriculum certification