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.
Not quite the one you need? Same words, different skill:
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.
What you can put on this worksheet
The exterior angle theorem
Find the exterior angle. — a triangle with one side extended to show an exterior angle, labeled 52°, 64°, x→ 116∘
Solve, then give the exterior angle
Find the measure of the exterior angle. — a triangle with one side extended to show an exterior angle, labeled 40°→ 84∘
A missing remote angle, x on all three, the angle beside it
Solve for x.— a triangle with one side extended to show an exterior angle, labeled 52°, 54°→ 11
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.
You pick from 3: the exterior angle theorem, solve, then give the exterior angle and a missing remote angle, x on all three, the angle beside it. Tick as many as you want and set how many of each, or let it spread them evenly.
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.