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Learn How to Solve Complementary and Vertical Angles Problems

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emily

5/28/2023

Geometry

7th Grade Types of Angles

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Geometry

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Angles

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Vertical, Complementary, and Supplementary Angles

Learn How to Solve Complementary and Vertical Angles Problems

This lesson covers key concepts in geometry, focusing on complementary angles, supplementary angles, and vertical angles. It provides definitions and examples for solving problems involving these angle relationships. The content is designed to help students understand and apply these concepts in geometric calculations.

• Complementary angles are angles that add up to 90 degrees.
• Supplementary angles are angles that add up to 180 degrees.
• Vertical angles are opposite angles formed by intersecting lines and are always equal.
• The lesson includes step-by-step examples for solving equations involving these angle relationships.
• Understanding these concepts is crucial for more advanced geometry and trigonometry topics.

...

5/28/2023

78

Complementary Angle An angle(s) that join together to equal 10° 56° 6x +3 2x+²7 ZABC=630 M 3n-8. Example 1: Solve for x X = 34° 26-6=20° 40

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Supplementary Angles

This page focuses on supplementary angles, building upon the knowledge of complementary angles from the previous section. It provides a definition and examples of solving supplementary angles equations.

Definition: Supplementary angles are angles that join together to equal 180°.

The page presents two detailed examples to illustrate the process of solving problems involving supplementary angles.

Example: In Example 1, we solve for x given two angles that form a supplementary pair: x° and 117°. The equation 4x + 7 + 5x + 1 = 180 is solved step-by-step, resulting in x = 63°.

Example: Example 2 demonstrates solving for x in the equation 9x + 18 = 180. The solution process leads to x = 18.

These examples provide students with practical applications of the supplementary angle concept, reinforcing their understanding of angle relationships and algebraic problem-solving in geometry.

Complementary Angle An angle(s) that join together to equal 10° 56° 6x +3 2x+²7 ZABC=630 M 3n-8. Example 1: Solve for x X = 34° 26-6=20° 40

View

Vertical Angles

The final page introduces the concept of vertical angles, completing the trio of angle relationships covered in this lesson. This section is crucial for solving vertical angles equations and understanding their properties.

Definition: Vertical angles are angles that are equal to each other when two lines intersect.

Vocabulary: The term "congruent" is introduced, meaning equal in the context of geometry.

The page provides a visual representation of vertical angles, showing two pairs of vertical angles formed by intersecting lines. It illustrates that when two lines intersect, the opposite angles are always equal.

Example: An example is given to solve for x in a vertical angle scenario. While the full solution is not provided in the transcript, it demonstrates how to set up the equation using the property of vertical angles being equal.

Highlight: The key takeaway from this section is that vertical angles are always congruent equalequal, which is a fundamental principle in geometry that students will use in more complex problems and proofs.

This concise yet informative page on vertical angles completes the lesson on angle relationships, providing students with a comprehensive understanding of complementary, supplementary, and vertical angles.

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Subjects

Geometry

Angles

Vertical, Complementary, and Supplementary Angles

 

Geometry

•

78

•

Jun 29, 2025

•

3 pages

Learn How to Solve Complementary and Vertical Angles Problems

user profile picture

emily

@emilyt31809

This lesson covers key concepts in geometry, focusing on complementary angles, supplementary angles, and vertical angles. It provides definitions and examples for solving problems involving these angle relationships. The content is designed to help students understand and apply these concepts... Show more

Complementary Angle An angle(s) that join together to equal 10° 56° 6x +3 2x+²7 ZABC=630 M 3n-8. Example 1: Solve for x X = 34° 26-6=20° 40

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Supplementary Angles

This page focuses on supplementary angles, building upon the knowledge of complementary angles from the previous section. It provides a definition and examples of solving supplementary angles equations.

Definition: Supplementary angles are angles that join together to equal 180°.

The page presents two detailed examples to illustrate the process of solving problems involving supplementary angles.

Example: In Example 1, we solve for x given two angles that form a supplementary pair: x° and 117°. The equation 4x + 7 + 5x + 1 = 180 is solved step-by-step, resulting in x = 63°.

Example: Example 2 demonstrates solving for x in the equation 9x + 18 = 180. The solution process leads to x = 18.

These examples provide students with practical applications of the supplementary angle concept, reinforcing their understanding of angle relationships and algebraic problem-solving in geometry.

Complementary Angle An angle(s) that join together to equal 10° 56° 6x +3 2x+²7 ZABC=630 M 3n-8. Example 1: Solve for x X = 34° 26-6=20° 40

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Vertical Angles

The final page introduces the concept of vertical angles, completing the trio of angle relationships covered in this lesson. This section is crucial for solving vertical angles equations and understanding their properties.

Definition: Vertical angles are angles that are equal to each other when two lines intersect.

Vocabulary: The term "congruent" is introduced, meaning equal in the context of geometry.

The page provides a visual representation of vertical angles, showing two pairs of vertical angles formed by intersecting lines. It illustrates that when two lines intersect, the opposite angles are always equal.

Example: An example is given to solve for x in a vertical angle scenario. While the full solution is not provided in the transcript, it demonstrates how to set up the equation using the property of vertical angles being equal.

Highlight: The key takeaway from this section is that vertical angles are always congruent equalequal, which is a fundamental principle in geometry that students will use in more complex problems and proofs.

This concise yet informative page on vertical angles completes the lesson on angle relationships, providing students with a comprehensive understanding of complementary, supplementary, and vertical angles.

Complementary Angle An angle(s) that join together to equal 10° 56° 6x +3 2x+²7 ZABC=630 M 3n-8. Example 1: Solve for x X = 34° 26-6=20° 40

Complementary Angles

This page introduces the concept of complementary angles and provides examples of how to solve complementary angles problems. Complementary angles are defined as angles that add up to 90 degrees.

Definition: Complementary angles are angles that join together to equal 90°.

The page presents three examples to illustrate the process of solving for unknown angles in complementary angle problems.

Example: In Example 1, we solve for x when given that x° + 56° = 90°. The solution shows that x = 34°.

Example: Example 2 demonstrates solving for x in the equation 6x + 3 + 2x + 17 = 90. The step-by-step solution leads to x = 10.

Example: The third example involves finding the measure of ∠QNP using the equation 3n - 2 + n + 6 = 90. The solution process results in n = 26.

These examples showcase different scenarios and equation types that students might encounter when working with complementary angles, providing a solid foundation for understanding supplementary angles examples as well.

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Paul T

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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 S

iOS 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 Klich

Android 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.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user