Worksheets · Geometry

Exterior angle theorem worksheet

Extend one side of a triangle and the angle outside equals the two interior angles it is not touching, added together. It follows from the angle sum, but it saves a step every time.

Select your difficulty

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

The Exterior Angle Theorem

Date Period

Find each missing value.

  1. Find the exterior angle58°20°x
  2. Find x79°70°8x + 21
  3. Find x45°105°6x + 60
  4. Find x44°41°6x - 5
  5. Find x44°86°6x + 46
  6. Find the exterior angle46°70°x
  7. Find the exterior angle37°39°x
  8. Find x53°79°7x + 13
  9. Find x66°84°6x + 48
  10. Find x39°58°8x - 7
  11. Find x55°29°7x - 7
  12. Find the exterior angle72°34°x
  13. Find x63°47°8x - 26
  14. Find the exterior angle76°58°x
  15. Find x70°76°8x + 42
  16. Find the exterior angle37°102°x
  17. Find x77°58°8x - 1
  18. Find x28°120°6x + 58
  19. Find the exterior angle44°48°x
  20. Find x51°62°8x - 23

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Exterior Angle TheoremAnswer keyVersion 1

Date Period

Find each missing value.

  1. Find the exterior angle58°20°x78
  2. Find x79°70°8x + 2116
  3. Find x45°105°6x + 6015
  4. Find x44°41°6x - 515
  5. Find x44°86°6x + 4614
  6. Find the exterior angle46°70°x116
  7. Find the exterior angle37°39°x76
  8. Find x53°79°7x + 1317
  9. Find x66°84°6x + 4817
  10. Find x39°58°8x - 713
  11. Find x55°29°7x - 713
  12. Find the exterior angle72°34°x106
  13. Find x63°47°8x - 2617
  14. Find the exterior angle76°58°x134
  15. Find x70°76°8x + 4213
  16. Find the exterior angle37°102°x139
  17. Find x77°58°8x - 117
  18. Find x28°120°6x + 5815
  19. Find the exterior angle44°48°x92
  20. Find x51°62°8x - 2317

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

How to do these

Remote interior angles of 50 and 65

  1. Add the two remote angles.
  2. Fifty plus sixty-five.
  3. That is the exterior angle.

The answer is 115.

Where students go wrong

Including the adjacent angle. The exterior angle equals the two it is far from, not the one beside it, and the one beside it is what makes 180 with it instead.

Also called remote interior angles or exterior angle of a triangle.

Questions about these worksheets

Yes. Every exterior angle theorem 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 exterior angle theorem 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.

Including the adjacent angle. The exterior angle equals the two it is far from, not the one beside it, and the one beside it is what makes 180 with it instead.