Two crossing lines make four angles. The pairs opposite each other are equal, and any two next to each other sit on a straight line and add to 180. Most questions give you two expressions for one of those pairs and ask for x.
Two angles form a linear pair. They measure 3x+10 and 2x+20. Find x
A linear pair adds to 180.
5x + 30 = 180.
5x = 150.
The answer is x=30.
Where students go wrong
Setting a linear pair equal to each other. Vertical angles are the equal ones. A linear pair sits on a straight line, so those add to 180 instead.
Also called vertical angles, linear pair, opposite angles or adjacent angles.
What you can put on this worksheet
Vertical angles
Find x→ 8
Linear pairs
Find x→ 8
Questions about these worksheets
Yes. Every vertical angles and linear pairs 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 vertical angles and linear pairs 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.
You pick from 2: vertical angles and linear pairs. Tick as many as you want and set how many of each, or let it spread them evenly.
Setting a linear pair equal to each other. Vertical angles are the equal ones. A linear pair sits on a straight line, so those add to 180 instead.