Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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

    15 · 2 · 180° · Polygon interior angle sums

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

    6 · 2 · 180° · Polygon interior angle sums

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

    22 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums

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

    11 · 2 · 180° · Polygon interior angle sums

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

    12 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    19 · 2 · 180° · Polygon interior angle sums

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

    13 · 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 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104731 · 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 15-sided polygon using (n − 2) × 180°.

    2340°

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

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

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

    3960°

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

12 questions · Seed 104731 · 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 15-sided polygon using (n − 2) × 180°.

    15 · 2 · 180° · Polygon interior angle sums

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

    6 · 2 · 180° · Polygon interior angle sums

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

    22 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums

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

    11 · 2 · 180° · Polygon interior angle sums

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

    12 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    19 · 2 · 180° · Polygon interior angle sums

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

    13 · 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 24-sided polygon using (n − 2) × 180°.

    24 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104731 · 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 15-sided polygon using (n − 2) × 180°.

    2340°

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

  2. 2. 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°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

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

    3960°

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

12 questions · Seed 104731 · Age guidance, not curriculum certification