Biology
Chemistry
AP Chemistry
English
AP English Literature
Geometry
Nov 30, 2025
268
4 pages
Mia @mialovesu16
Get ready to master central angles, arc measures, and arc lengths in circles! These concepts are foundational for... Show more
Ever wonder how angles in a circle relate to the arcs they create? A central angle has its vertex at the center of the circle with its sides forming radii. All central angles in a circle add up to 360°.
When you have a central angle, the measure of the arc it creates equals the measure of the central angle itself. For example, if angle AOB is 84°, then the arc AB is also 84°. This direct relationship makes calculating arc measures straightforward once you know the central angle.
Finding unknown angles often involves using what you know about circles. If you're given some angle measures, you can find others by subtracting from 360° or using other angle relationships. For problems with algebraic expressions like °, you'll need to set up equations using the fact that angles in a circle sum to 360°.
💡 Quick Tip When solving for unknown angles in a circle, always remember that the measure of an arc equals the measure of its central angle. This one-to-one relationship is your key to solving most circle problems!
Arc length is basically a portion of the circumference - imagine cutting out a slice of the circle's edge. To find it, you'll use the formula arc length = 2πr, where x is the degree measure of the arc.
Working with arc lengths connects your knowledge of circles with real-world measurements. For example, if a circle has radius 15 cm and you need to find the length of an arc measuring 112°, just plug into the formula 2π(15)(112/360) ≈ 29.32 cm. This tells you exactly how long that portion of the circle is.
Practice problems like these prepare you for real applications. Whether you're finding the length of a curved road section on a map or calculating how much material you need for a curved design, these skills are directly applicable.
🔑 Remember The arc length formula is just a portion of the full circumference formula (2πr). Think of it as finding what fraction of the whole circle your arc represents!
Finding arc measures helps you determine the size of sections of a circle. When you know central angles, you can immediately determine the arc measures - they're the same value!
Sometimes you'll need to find complementary or supplementary arcs. For example, if an arc measures 76°, its complementary arc (the rest of the semicircle) would be 180° - 76° = 104°. If you need the remaining portion of the full circle, you'd calculate 360° - 76° = 284°.
Algebraic expressions in arc problems require you to set up equations based on what you know about circles. When you see expressions like °, you'll typically use the fact that angles around a point sum to 180° or angles in a circle sum to 360°. Solving for x allows you to find the actual measure of each arc.
💡 Strategy Tip When multiple arcs are given with expressions, create an equation using their sum. If they form a semicircle, they sum to 180°. If they make a complete circle, they sum to 360°.
Arc problems often require multiple steps to solve. First, you'll solve algebraic equations to find the value of x, then substitute that value back to calculate specific arc measures. This two-step approach helps break down complex problems.
When working with multiple arcs, keep track of which arcs form complete circles or semicircles. For example, in problem 10, the sum of all central angles equals 360°, which helps you set up the equation 90° + 12x° + ° + ° = 360°.
Arc length problems combine your knowledge of central angles with the formula for circumference. For a circle with radius r and an arc of measure x°, the arc length equals 2πr. For example, if a circle has radius 11 ft and an arc measures 211°, the arc length is approximately 40.51 ft.
🌟 Pro Tip Draw a diagram when solving arc problems! Sketching the circle and labeling the arcs makes it much easier to visualize the relationships between different parts of the circle and avoid calculation errors.
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
This is a finished and completed worksheet that applies very helpful information for the subject.
GeometryThis is a finished and completed worksheet that applies very helpful information for the subject.
GeometryU10L2 Central Angles & Arc Measures Solutions
GeometryApp Store
Google 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 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
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
Mia
@mialovesu16
Get ready to master central angles, arc measures, and arc lengths in circles! These concepts are foundational for understanding circle geometry and will help you solve problems involving circular objects in real life and in future math courses.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wonder how angles in a circle relate to the arcs they create? A central angle has its vertex at the center of the circle with its sides forming radii. All central angles in a circle add up to 360°.
When you have a central angle, the measure of the arc it creates equals the measure of the central angle itself. For example, if angle AOB is 84°, then the arc AB is also 84°. This direct relationship makes calculating arc measures straightforward once you know the central angle.
Finding unknown angles often involves using what you know about circles. If you're given some angle measures, you can find others by subtracting from 360° or using other angle relationships. For problems with algebraic expressions like °, you'll need to set up equations using the fact that angles in a circle sum to 360°.
💡 Quick Tip: When solving for unknown angles in a circle, always remember that the measure of an arc equals the measure of its central angle. This one-to-one relationship is your key to solving most circle problems!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Arc length is basically a portion of the circumference - imagine cutting out a slice of the circle's edge. To find it, you'll use the formula: arc length = 2πr, where x is the degree measure of the arc.
Working with arc lengths connects your knowledge of circles with real-world measurements. For example, if a circle has radius 15 cm and you need to find the length of an arc measuring 112°, just plug into the formula: 2π(15)(112/360) ≈ 29.32 cm. This tells you exactly how long that portion of the circle is.
Practice problems like these prepare you for real applications. Whether you're finding the length of a curved road section on a map or calculating how much material you need for a curved design, these skills are directly applicable.
🔑 Remember: The arc length formula is just a portion of the full circumference formula (2πr). Think of it as finding what fraction of the whole circle your arc represents!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Finding arc measures helps you determine the size of sections of a circle. When you know central angles, you can immediately determine the arc measures - they're the same value!
Sometimes you'll need to find complementary or supplementary arcs. For example, if an arc measures 76°, its complementary arc (the rest of the semicircle) would be 180° - 76° = 104°. If you need the remaining portion of the full circle, you'd calculate 360° - 76° = 284°.
Algebraic expressions in arc problems require you to set up equations based on what you know about circles. When you see expressions like °, you'll typically use the fact that angles around a point sum to 180° or angles in a circle sum to 360°. Solving for x allows you to find the actual measure of each arc.
💡 Strategy Tip: When multiple arcs are given with expressions, create an equation using their sum. If they form a semicircle, they sum to 180°. If they make a complete circle, they sum to 360°.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Arc problems often require multiple steps to solve. First, you'll solve algebraic equations to find the value of x, then substitute that value back to calculate specific arc measures. This two-step approach helps break down complex problems.
When working with multiple arcs, keep track of which arcs form complete circles or semicircles. For example, in problem 10, the sum of all central angles equals 360°, which helps you set up the equation: 90° + 12x° + ° + ° = 360°.
Arc length problems combine your knowledge of central angles with the formula for circumference. For a circle with radius r and an arc of measure x°, the arc length equals 2πr. For example, if a circle has radius 11 ft and an arc measures 211°, the arc length is approximately 40.51 ft.
🌟 Pro Tip: Draw a diagram when solving arc problems! Sketching the circle and labeling the arcs makes it much easier to visualize the relationships between different parts of the circle and avoid calculation errors.
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
This is a finished and completed worksheet that applies very helpful information for the subject.
GeometryThis is a finished and completed worksheet that applies very helpful information for the subject.
GeometryU10L2 Central Angles & Arc Measures Solutions
GeometryApp Store
Google 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 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
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
Calculus 1
Algebra 1
Overige