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MathsAges 16-18

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 16-18

Polygon interior angle sums

Take your time. Show your thinking.

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

    30 · 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 14-sided polygon using (n − 2) × 180°.

    14 · 2 · 180° · Polygon interior angle sums

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

    21 · 2 · 180° · Polygon interior angle sums

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

    12 · 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 27-sided polygon using (n − 2) × 180°.

    27 · 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 11-sided polygon using (n − 2) × 180°.

    11 · 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 6-sided polygon using (n − 2) × 180°.

    6 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 55 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. 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°.

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

    2160°

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

  4. 4. 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°.

  5. 5. 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°.

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

    4500°

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

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

    1620°

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

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

    720°

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

  12. 12. 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°.

12 questions · Seed 55 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Polygon interior angle sums

Take your time. Show your thinking.

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

    30 · 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 14-sided polygon using (n − 2) × 180°.

    14 · 2 · 180° · Polygon interior angle sums

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

    21 · 2 · 180° · Polygon interior angle sums

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

    12 · 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 27-sided polygon using (n − 2) × 180°.

    27 · 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 11-sided polygon using (n − 2) × 180°.

    11 · 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 6-sided polygon using (n − 2) × 180°.

    6 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 55 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Polygon interior angle sums

Answers and reasoning. Review before teaching.

  1. 1. 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°.

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

    2160°

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

  4. 4. 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°.

  5. 5. 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°.

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

    4500°

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

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

    1620°

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

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

    720°

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

  12. 12. 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°.

12 questions · Seed 55 · Age guidance, not curriculum certification