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.
Not quite the one you need? Same words, different skill:
Angle Relationships (Geometry). Angle pairs, angles around a point, three lines through one point.
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Vertical Angles and Linear PairsAnswer keyVersion 1
Date Period
Find each measure.
Use vertical angles and linear pairs
The figure shows two intersecting lines. Solve for x.9
The two lines cross. What is the measure of the angle marked y?67∘
In the figure, two lines cross. Find x.21
Find the value of x.61∘
Two lines meet at a point. Solve for x.15
Use linear pairs
Find the angle marked 7x+32.137∘
The two lines cross. What is y?82∘
The ray stands on a straight line. Find x.11
Two straight lines intersect. What is the value of x?16
Find the angle marked y.73∘
Find x and all four angles
Two lines cross. One angle measures (3x+24)∘ and an angle next to it (a linear pair) measures (6x+39)∘.Find x and all four angles.x=13;63∘,63∘,117∘,117∘
Two lines cross. One angle measures (6x−14)∘ and the angle vertical to it measures (x+16)∘.Find x and all four angles.x=6;22∘,22∘,158∘,158∘
Two lines cross. One angle measures (6x+38)∘ and an angle next to it (a linear pair) measures (3x−2)∘.Find x and all four angles.x=16;46∘,46∘,134∘,134∘
Two lines cross. One angle measures (6x−13)∘ and an angle next to it (a linear pair) measures (5x+28)∘.Find x and all four angles.x=15;77∘,77∘,103∘,103∘
Two lines cross. One angle measures (3x+29)∘ and the angle vertical to it measures (7x−43)∘.Find x and all four angles.x=18;83∘,83∘,97∘,97∘
Find angles where three lines meet
Three straight lines pass through the same point. Find x.70
Three lines cross at one point. Find the angle marked (3x+50)∘.80∘
The lines cross at one point, making six angles. What is the measure of the angle marked (x+44)∘?56∘
Three lines meet at a point. What is x?3
Three straight lines pass through the same point. What is the measure of the angle marked (2x+41)∘?69∘
Two angles form a linear pair. They measure 3x+10and 2x+20.Find x
A linear pair adds to 180.
5x + 30 = 180.
5x = 150.
The answer is 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
Two straight lines intersect. Find x.— two lines crossing, with the four angles marked→ 11
Linear pairs
What is y?— two angles, y and 84°, on a straight line→ 96∘
All four angles
Two lines cross. One angle measures (5x−25)∘ and the angle vertical to it measures (4x−6)∘.Find x and all four angles.→ x=19;70∘,70∘,110∘,110∘
Three lines through one point
What is x?— rays from one point, with the angles between them marked, labeled 67°→ 3
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 4: vertical angles, linear pairs, all four angles and three lines through one point. 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.