Worksheets · Geometry

Angles in quadrilaterals worksheet

Any quadrilateral splits into two triangles, so its angles add to twice 180. That single fact answers every question on the page, whether the angles are numbers or expressions.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Angles in Quadrilaterals

Date Period

Find each missing value.

  1. Find the fourth angle40°87°129°xABCD
  2. Find the fourth angle65°95°105°xABCD
  3. Find the fourth angle112°66°58°xABCD
  4. Find the fourth angle89°109°57°xABCD
  5. Find the fourth angle81°110°130°xABCD
  6. Find the fourth angle118°61°130°xABCD
  7. Find the fourth angle76°67°101°xABCD
  8. Find the fourth angle124°103°123°xABCD
  9. Find the fourth angle124°50°43°xABCD
  10. Find the fourth angle66°120°86°xABCD
  11. Find the fourth angle104°55°101°xABCD
  12. Find the fourth angle52°128°54°xABCD
  13. Find x2x + 33°2x + 34°3x + 9°172°ABCD
  14. Find the fourth angle117°64°54°xABCD
  15. Find x2x + 35°x + 23°3x + 11°171°ABCD
  16. Find x2x + 11°3x + 33°3x + 34°154°ABCD
  17. Find x2x + 53°4x + 5°4x + 15°97°ABCD
  18. Find x2x + 10°3x + 19°4x + 53°98°ABCD
  19. Find the fourth angle112°60°48°xABCD
  20. Find x3x + 22°2x + 55°4x + 53°68°ABCD

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

Sigma Prep · sigmaprep.io/worksheets

Name

Angles in QuadrilateralsAnswer keyVersion 1

Date Period

Find each missing value.

  1. Find the fourth angle40°87°129°xABCD104
  2. Find the fourth angle65°95°105°xABCD95
  3. Find the fourth angle112°66°58°xABCD124
  4. Find the fourth angle89°109°57°xABCD105
  5. Find the fourth angle81°110°130°xABCD39
  6. Find the fourth angle118°61°130°xABCD51
  7. Find the fourth angle76°67°101°xABCD116
  8. Find the fourth angle124°103°123°xABCD10
  9. Find the fourth angle124°50°43°xABCD143
  10. Find the fourth angle66°120°86°xABCD88
  11. Find the fourth angle104°55°101°xABCD100
  12. Find the fourth angle52°128°54°xABCD126
  13. Find x2x + 33°2x + 34°3x + 9°172°ABCD16
  14. Find the fourth angle117°64°54°xABCD125
  15. Find x2x + 35°x + 23°3x + 11°171°ABCD20
  16. Find x2x + 11°3x + 33°3x + 34°154°ABCD16
  17. Find x2x + 53°4x + 5°4x + 15°97°ABCD19
  18. Find x2x + 10°3x + 19°4x + 53°98°ABCD20
  19. Find the fourth angle112°60°48°xABCD140
  20. Find x3x + 22°2x + 55°4x + 53°68°ABCD18

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

How to do these

Three angles are 80,95,110

  1. The four add to 360.
  2. Those three add to 285.
  3. Subtract from 360.

The answer is 75.

Where students go wrong

Using 180. That is the triangle sum; a quadrilateral is two triangles, so it is 360, and using the wrong one halves every answer.

Also called quadrilateral angle sum, missing angle in a quadrilateral or find x quadrilateral.

Questions about these worksheets

Yes. Every angles in quadrilaterals 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 angles in quadrilaterals 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 two 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.

Using 180. That is the triangle sum; a quadrilateral is two triangles, so it is 360, and using the wrong one halves every answer.