When lines intersect, they create different types of angles with...
Mathematics103 views·Updated Jun 15, 2026·2 pagesUnderstanding Adjacent and Vertical Angles
1
of 2
Adjacent and Vertical Angles
Ever notice how angles form when lines cross each other? These angles have special relationships! Adjacent angles share a common side and vertex (corner point). Think of them like neighbors sharing a fence between their yards.
Vertical angles are opposite angles formed when two lines intersect. The cool thing about vertical angles is they're always congruent - meaning they have exactly the same measurement. This is super helpful when solving geometry problems!
You can identify these angles by their positions. For example, if you have intersecting lines forming angles 1, 2, 3, and 4, angles 1 and 3 would be vertical angles (opposite each other). Angles that share a side, like angles 1 and 2, are adjacent.
Helpful Tip: When identifying adjacent angles, remember they must share both a side AND a vertex. Just being next to each other isn't enough!
2
of 2
Finding Angle Measurements
You can use what you know about adjacent and vertical angles to find missing measurements. For vertical angles, remember they're always equal - if one vertical angle is 70°, its opposite angle is also 70°!
Adjacent angles often form special relationships too. Sometimes they form a straight line (180°) or a right angle (90°). When adjacent angles form a right angle, they're called complementary angles and add up to 90°.
To solve angle problems, write an equation using what you know. For example, if adjacent angles measure 31° and °, and they form a right angle, then + 31 = 90. Solving this equation gives you x = 55.
Problem-Solving Strategy: When drawing vertical angles, remember to create intersecting lines with the same measurement on opposite angles. The angles across from each other must be identical!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
9M
MathematicsMath Made Easy: Essential Concepts for Grade 7
Master key math concepts with this comprehensive flashcard set designed specifically for 7th graders. Boost your understanding and ace your exams!
7th7201
C
MathematicsChapter 2 Quiz. Algebra 1
Equations with variables on both side, literal equations, ratios, conversions, proportions
9th4672
M
GeometryMath Flashcards: Triangles, Angles, and Congruent Triangles
Master the fundamentals of geometry with these math flashcards covering triangle angles, parallel lines, and congruent triangles. Test your knowledge and ace your exams!
10th2520
G
GeometryGeometry Flashcards: Triangles, Proofs, Angles, and Lines
Master the fundamentals of geometry with these flashcards covering triangles, proofs, angles, and parallel lines. Test your knowledge and ace your exams!
9th3050
G
GeometryGeometry Essentials
Master the fundamentals of geometry with these flashcards covering angles, triangles, congruent triangles, parallel lines, and polygons.
10th3410
S
MathematicsSolving X on both sides of an equation
Solve for x when there is x on both sides of equation.
9th2721
B
MathematicsBasic multiplication and division
like 6th grade math
6th46010
P
MathematicsPEMDAS
PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) Order of operation to solve math problems.
6th3790
M
Mathematicsmath
learn some new math
6th4003
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7390
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
O
AP World HistoryOrigins and Continuity of the Byzantine Empire
Analyze the political and cultural transitions from the Roman Empire to the Byzantine Empire, focusing on the reign of Justinian I and his code.
9th1,6320
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Mathematics103 views·Updated Jun 15, 2026·2 pagesUnderstanding Adjacent and Vertical Angles
When lines intersect, they create different types of angles with special relationships. Understanding adjacent and vertical angles helps you solve geometry problems and recognize patterns in shapes all around you!
1
of 2
Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Adjacent and Vertical Angles
Ever notice how angles form when lines cross each other? These angles have special relationships! Adjacent angles share a common side and vertex (corner point). Think of them like neighbors sharing a fence between their yards.
Vertical angles are opposite angles formed when two lines intersect. The cool thing about vertical angles is they're always congruent - meaning they have exactly the same measurement. This is super helpful when solving geometry problems!
You can identify these angles by their positions. For example, if you have intersecting lines forming angles 1, 2, 3, and 4, angles 1 and 3 would be vertical angles (opposite each other). Angles that share a side, like angles 1 and 2, are adjacent.
Helpful Tip: When identifying adjacent angles, remember they must share both a side AND a vertex. Just being next to each other isn't enough!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Finding Angle Measurements
You can use what you know about adjacent and vertical angles to find missing measurements. For vertical angles, remember they're always equal - if one vertical angle is 70°, its opposite angle is also 70°!
Adjacent angles often form special relationships too. Sometimes they form a straight line (180°) or a right angle (90°). When adjacent angles form a right angle, they're called complementary angles and add up to 90°.
To solve angle problems, write an equation using what you know. For example, if adjacent angles measure 31° and °, and they form a right angle, then + 31 = 90. Solving this equation gives you x = 55.
Problem-Solving Strategy: When drawing vertical angles, remember to create intersecting lines with the same measurement on opposite angles. The angles across from each other must be identical!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
9M
MathematicsMath Made Easy: Essential Concepts for Grade 7
Master key math concepts with this comprehensive flashcard set designed specifically for 7th graders. Boost your understanding and ace your exams!
7th7201
C
MathematicsChapter 2 Quiz. Algebra 1
Equations with variables on both side, literal equations, ratios, conversions, proportions
9th4672
M
GeometryMath Flashcards: Triangles, Angles, and Congruent Triangles
Master the fundamentals of geometry with these math flashcards covering triangle angles, parallel lines, and congruent triangles. Test your knowledge and ace your exams!
10th2520
G
GeometryGeometry Flashcards: Triangles, Proofs, Angles, and Lines
Master the fundamentals of geometry with these flashcards covering triangles, proofs, angles, and parallel lines. Test your knowledge and ace your exams!
9th3050
G
GeometryGeometry Essentials
Master the fundamentals of geometry with these flashcards covering angles, triangles, congruent triangles, parallel lines, and polygons.
10th3410
S
MathematicsSolving X on both sides of an equation
Solve for x when there is x on both sides of equation.
9th2721
B
MathematicsBasic multiplication and division
like 6th grade math
6th46010
P
MathematicsPEMDAS
PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) Order of operation to solve math problems.
6th3790
M
Mathematicsmath
learn some new math
6th4003
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7390
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
O
AP World HistoryOrigins and Continuity of the Byzantine Empire
Analyze the political and cultural transitions from the Roman Empire to the Byzantine Empire, focusing on the reign of Justinian I and his code.
9th1,6320
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user