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

    19 · 2 · 180° · Polygon interior angle sums

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

    8 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    27 · 2 · 180° · Polygon interior angle sums

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

    13 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    7 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

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

    17 · 2 · 180° · Polygon interior angle sums

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

    25 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104732 · 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 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 19-sided polygon using (n − 2) × 180°.

    3060°

    Substitute n = 19: (19 − 2) × 180° = 17 × 180° = 3060°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

  11. 11. 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°.

  12. 12. 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°.

12 questions · Seed 104732 · 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 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 19-sided polygon using (n − 2) × 180°.

    19 · 2 · 180° · Polygon interior angle sums

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

    8 · 2 · 180° · Polygon interior angle sums

  4. 4. Calculate the sum of the interior angles of a 27-sided polygon using (n − 2) × 180°.

    27 · 2 · 180° · Polygon interior angle sums

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

    13 · 2 · 180° · Polygon interior angle sums

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

    9 · 2 · 180° · Polygon interior angle sums

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

    7 · 2 · 180° · Polygon interior angle sums

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

    20 · 2 · 180° · Polygon interior angle sums

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

    23 · 2 · 180° · Polygon interior angle sums

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

    17 · 2 · 180° · Polygon interior angle sums

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

    25 · 2 · 180° · Polygon interior angle sums

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

    26 · 2 · 180° · Polygon interior angle sums
12 questions · Seed 104732 · 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 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 19-sided polygon using (n − 2) × 180°.

    3060°

    Substitute n = 19: (19 − 2) × 180° = 17 × 180° = 3060°.

  3. 3. 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°.

  4. 4. 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°.

  5. 5. 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°.

  6. 6. 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°.

  7. 7. 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°.

  8. 8. 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°.

  9. 9. 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°.

  10. 10. 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°.

  11. 11. 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°.

  12. 12. 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°.

12 questions · Seed 104732 · Age guidance, not curriculum certification