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Maths
1 Dec 2025
197
2 pages
Scarlett Edwardes @scarlett_1917
Ever wondered why a triangle's angles always add up to 180°, or what happens when you add more... Show more
Here's something brilliant interior angles in any polygon follow a dead simple formula. Just take the number of sides, subtract 2, then multiply by 180°. So the formula is × 180° where n equals your sides.
Exterior angles are even easier! They always add up to 360° total, so each one equals 360° ÷ n. Whether you're dealing with a triangle or a dodecagon, these rules never fail.
Let's see this in action with an 8-sided polygon (called an octagon). First, we count our sides - that's 8. Then we subtract 2, giving us 6.
Quick Tip Remember that exterior angles always total 360° - imagine walking around the outside of any shape and you'll always make one complete turn!
Now we multiply that 6 by 180°, which gives us 1080°. That's the total of all interior angles in an octagon - pretty massive compared to a triangle's 180°!
For exterior angles in the same octagon, we use our second rule. Take 360° and divide by 8 sides, giving us 45° for each exterior angle.
The beauty of these formulas is they work every single time. Pentagon? (5-2) × 180° = 540°. Hexagon? (6-2) × 180° = 720°. You've got this!
Memory Trick Interior angles get bigger as shapes get more sides, but exterior angles get smaller - they're sharing that same 360° between more corners!
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the calculations of interior and exterior angles in polygons, including regular polygons. This summary covers key formulas, examples for hexagons and heptagons, and step-by-step solutions to find angle measures. Ideal for students studying geometry.
MathsExplore the concepts of interior and exterior angles in polygons. This summary covers definitions, examples, and the formulas for calculating the sum of interior angles based on the number of sides. Ideal for students studying geometry.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsApp 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Scarlett Edwardes
@scarlett_1917
Ever wondered why a triangle's angles always add up to 180°, or what happens when you add more sides? Understanding polygon angles is actually quite straightforward once you know the two simple rules that work for any shape.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Here's something brilliant: interior angles in any polygon follow a dead simple formula. Just take the number of sides, subtract 2, then multiply by 180°. So the formula is × 180° where n equals your sides.
Exterior angles are even easier! They always add up to 360° total, so each one equals 360° ÷ n. Whether you're dealing with a triangle or a dodecagon, these rules never fail.
Let's see this in action with an 8-sided polygon (called an octagon). First, we count our sides - that's 8. Then we subtract 2, giving us 6.
Quick Tip: Remember that exterior angles always total 360° - imagine walking around the outside of any shape and you'll always make one complete turn!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Now we multiply that 6 by 180°, which gives us 1080°. That's the total of all interior angles in an octagon - pretty massive compared to a triangle's 180°!
For exterior angles in the same octagon, we use our second rule. Take 360° and divide by 8 sides, giving us 45° for each exterior angle.
The beauty of these formulas is they work every single time. Pentagon? (5-2) × 180° = 540°. Hexagon? (6-2) × 180° = 720°. You've got this!
Memory Trick: Interior angles get bigger as shapes get more sides, but exterior angles get smaller - they're sharing that same 360° between more corners!
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the calculations of interior and exterior angles in polygons, including regular polygons. This summary covers key formulas, examples for hexagons and heptagons, and step-by-step solutions to find angle measures. Ideal for students studying geometry.
MathsExplore the concepts of interior and exterior angles in polygons. This summary covers definitions, examples, and the formulas for calculating the sum of interior angles based on the number of sides. Ideal for students studying geometry.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsApp 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
