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18
1
Kimberley
13/09/2025
Maths
Angles in Circles
765
•
13 Sept 2025
•
Learn About Circles and Angles: Easy Guide for Kids
Kimberley
@kimberley_ncyf
1 / 2
Page 2: Angle Calculations and Triangle Properties
This page focuses on techniques for finding missing angles in geometric figures involving circles and triangles. It provides a step-by-step approach to solving angle-related problems.
The first step in finding missing angles is to identify and fill in all known angles from the given diagram. This includes recognizing right angles based on the properties discussed on the previous page.
Highlight: When solving angle problems, start by identifying all known angles, especially right angles formed by tangents or inscribed triangles on diameters.
The page emphasizes the importance of using triangle properties to find missing angles. This includes understanding the characteristics of isosceles triangles, which have two equal angles opposite the equal sides.
Definition: An isosceles triangle is a triangle with at least two equal sides and two equal angles.
The concept of vertically opposite angles is introduced. These are angles formed when two lines intersect, and they are always equal to each other.
Vocabulary: Vertically opposite angles are pairs of angles formed when two lines intersect, and they are always congruent (equal).
The page also mentions the straight angle property, which states that angles on a straight line add up to 180°. This is a crucial concept for solving many angle problems.
Example: If two angles on a straight line are known to be 70° and 50°, the third angle can be calculated as 180° - = 60°.
Lastly, the page touches on the fact that the three angles in any triangle always sum to 180°. This property, combined with the others mentioned, provides a powerful toolkit for solving complex angle problems in geometry.
Highlight: Remember that the sum of angles in any triangle is always 180°, which is essential for حساب زوايا المثلث (calculating triangle angles).
Page 1: Circle Properties and Angle Relationships
This page introduces fundamental concepts about circles and their relationships with angles and lines. It covers several key properties that are essential for understanding circle geometry.
Definition: A diameter is a line segment that passes through the center of a circle and has its endpoints on the circle.
The page explains that when a triangle is inscribed in a circle with one side as the diameter, the angle opposite to this side is always a right angle (90°). This property is known as the خصائص نصف الدائرة (properties of a semicircle).
Highlight: If a triangle sits on the diameter of a circle, the angle touching the circle's circumference is always 90° (a right angle).
The concept of tangents is also introduced. A tangent is a line that touches the circle at exactly one point. The page notes that a tangent line is always perpendicular (forms a 90° angle) to the radius at the point of contact.
Vocabulary: A tangent is a line that touches a circle at a single point without crossing into the circle's interior.
The page also discusses radii (plural of radius) and their properties. All radii in a circle have the same length, which is a fundamental characteristic of circles.
Definition: A radius is a line segment from the center of a circle to any point on its circumference.
Lastly, the page mentions that a triangle formed by two radii of a circle is always isosceles. This is because two sides of the triangle (the radii) are equal in length.
Example: In a circle, a triangle formed by two radii and a chord is always isosceles because the two radii are equal in length.
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4.9/5
App Store
4.8/5
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
Learn About Circles and Angles: Easy Guide for Kids
Kimberley
@kimberley_ncyf
The circle is a fundamental geometric shape with unique properties and applications in mathematics and everyday life. This guide explores key concepts related to circles, angles, and triangles, providing essential information for students studying geometry.
- Circles have special properties involving... Show more
Page 2: Angle Calculations and Triangle Properties
This page focuses on techniques for finding missing angles in geometric figures involving circles and triangles. It provides a step-by-step approach to solving angle-related problems.
The first step in finding missing angles is to identify and fill in all known angles from the given diagram. This includes recognizing right angles based on the properties discussed on the previous page.
Highlight: When solving angle problems, start by identifying all known angles, especially right angles formed by tangents or inscribed triangles on diameters.
The page emphasizes the importance of using triangle properties to find missing angles. This includes understanding the characteristics of isosceles triangles, which have two equal angles opposite the equal sides.
Definition: An isosceles triangle is a triangle with at least two equal sides and two equal angles.
The concept of vertically opposite angles is introduced. These are angles formed when two lines intersect, and they are always equal to each other.
Vocabulary: Vertically opposite angles are pairs of angles formed when two lines intersect, and they are always congruent (equal).
The page also mentions the straight angle property, which states that angles on a straight line add up to 180°. This is a crucial concept for solving many angle problems.
Example: If two angles on a straight line are known to be 70° and 50°, the third angle can be calculated as 180° - = 60°.
Lastly, the page touches on the fact that the three angles in any triangle always sum to 180°. This property, combined with the others mentioned, provides a powerful toolkit for solving complex angle problems in geometry.
Highlight: Remember that the sum of angles in any triangle is always 180°, which is essential for حساب زوايا المثلث (calculating triangle angles).
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Page 1: Circle Properties and Angle Relationships
This page introduces fundamental concepts about circles and their relationships with angles and lines. It covers several key properties that are essential for understanding circle geometry.
Definition: A diameter is a line segment that passes through the center of a circle and has its endpoints on the circle.
The page explains that when a triangle is inscribed in a circle with one side as the diameter, the angle opposite to this side is always a right angle (90°). This property is known as the خصائص نصف الدائرة (properties of a semicircle).
Highlight: If a triangle sits on the diameter of a circle, the angle touching the circle's circumference is always 90° (a right angle).
The concept of tangents is also introduced. A tangent is a line that touches the circle at exactly one point. The page notes that a tangent line is always perpendicular (forms a 90° angle) to the radius at the point of contact.
Vocabulary: A tangent is a line that touches a circle at a single point without crossing into the circle's interior.
The page also discusses radii (plural of radius) and their properties. All radii in a circle have the same length, which is a fundamental characteristic of circles.
Definition: A radius is a line segment from the center of a circle to any point on its circumference.
Lastly, the page mentions that a triangle formed by two radii of a circle is always isosceles. This is because two sides of the triangle (the radii) are equal in length.
Example: In a circle, a triangle formed by two radii and a chord is always isosceles because the two radii are equal in length.
We thought you’d never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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.
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4.9/5
App Store
4.8/5
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