Worksheets · Geometry

Polygons and angles worksheet

The interior angles of an n-sided polygon add to n minus two, times 180. The exterior angles always add to 360 however many sides there are, which surprises people every time.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Polygons and Angles

Date Period

Find each measure.

  1. Find the sum of the interior angles
  2. Find each interior angle of a regular icosagon
  3. Find each interior angle of a regular decagon
  4. Find each exterior angle of a regular icosagon
  5. Find each exterior angle of a regular quadrilateral
  6. Find each interior angle of a regular octagon
  7. Find the sum of the interior angles of a pentagon
  8. Find each exterior angle
  9. Find the sum of the interior angles
  10. Find each interior angle
  11. Find each interior angle of a regular pentagon
  12. Find each exterior angle of a regular hexagon
  13. Find each interior angle
  14. Find the sum of the interior angles of a quadrilateral
  15. Find each interior angle
  16. Find each interior angle
  17. Find each interior angle
  18. Find the sum of the interior angles
  19. Find each interior angle of a regular dodecagon
  20. Find the sum of the interior angles of a icosagon

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Polygons and AnglesAnswer keyVersion 1

Date Period

Find each measure.

  1. Find the sum of the interior angles1440
  2. Find each interior angle of a regular icosagon162
  3. Find each interior angle of a regular decagon144
  4. Find each exterior angle of a regular icosagon18
  5. Find each exterior angle of a regular quadrilateral90
  6. Find each interior angle of a regular octagon135
  7. Find the sum of the interior angles of a pentagon540
  8. Find each exterior angle72
  9. Find the sum of the interior angles2340
  10. Find each interior angle135
  11. Find each interior angle of a regular pentagon108
  12. Find each exterior angle of a regular hexagon60
  13. Find each interior angle90
  14. Find the sum of the interior angles of a quadrilateral360
  15. Find each interior angle120
  16. Find each interior angle162
  17. Find each interior angle160
  18. Find the sum of the interior angles360
  19. Find each interior angle of a regular dodecagon150
  20. Find the sum of the interior angles of a icosagon3240

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the sum of the interior angles of a 7-sided polygon

  1. Subtract 2 from the number of sides.
  2. Multiply by 180.

The answer is 900.

Where students go wrong

Multiplying by the number of sides rather than two fewer. A pentagon is 540, not 900, and the quickest sanity check is a triangle: three sides has to give 180.

Also called interior angle sum, exterior angles or regular polygons.

Questions about these worksheets

Yes. Every polygons and angles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the polygons and angles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Multiplying by the number of sides rather than two fewer. A pentagon is 540, not 900, and the quickest sanity check is a triangle: three sides has to give 180.