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Fun with Angles: Triangles and Polygons Explained

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Luke

19/10/2022

Maths

Angle Facts Revision Sheet

Fun with Angles: Triangles and Polygons Explained

This document covers key geometric concepts related to angles in various shapes. It provides essential formulas and rules for understanding angle relationships in triangles, quadrilaterals, and polygons.

  • Angles in triangles and their properties
  • Angles in quadrilaterals and around points
  • Relationships between different types of angles
  • Formulas for interior and exterior angles of polygons
...

19/10/2022

709

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Maths

709

19 Oct 2022

1 page

Fun with Angles: Triangles and Polygons Explained

This document covers key geometric concepts related to angles in various shapes. It provides essential formulas and rules for understanding angle relationships in triangles, quadrilaterals, and polygons.

  • Angles in triangles and their properties
  • Angles in quadrilaterals and around points
  • Relationships... Show more

a+6+c=1800
a = b
a
a = 60°
a+b+c+d=360°
a+b+c=1800
Angles in a
triangle add
up to 1800
Base angles in an
isoceles triangle
are equal
désé
Al

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Geometric Angle Relationships and Formulas

This page presents a comprehensive overview of fundamental geometric concepts related to angles in various shapes. It covers essential formulas and rules for understanding angle relationships in triangles, quadrilaterals, and polygons.

Highlight: The document provides a quick reference guide for key angle facts and formulas in geometry.

Triangle Angles

The page begins by discussing angles in triangles:

Definition: Angles in a triangle add up to 180°.

This is a fundamental principle in geometry. The document also mentions specific types of triangles:

Vocabulary: In an isosceles triangle, the base angles are equal.

Example: In an equilateral triangle, all angles are equal and measure 60°.

Quadrilateral Angles

Moving on to quadrilaterals, the document states:

Definition: Angles in a quadrilateral add up to 360°.

This is another crucial concept in geometry, applicable to all four-sided shapes.

Angles on Lines and Around Points

The page covers several important angle relationships:

  1. Angles on a straight line add up to 180°.
  2. Angles around a point add up to 360°.
  3. Vertically opposite angles are equal.
  4. Alternate angles are equal ZruleZ-rule.
  5. Corresponding angles are equal FruleF-rule.
  6. Supplementary angles add up to 180° CruleC-rule.

These relationships are fundamental in understanding angle properties in various geometric configurations.

Polygon Angles

The document concludes with formulas for angles in polygons:

Definition: The sum of exterior angles of a polygon is always 360°.

Highlight: Sum of interior angles of a polygon formula: n2n-2 × 180°, where n is the number of sides.

Vocabulary: For a regular polygon, the exterior angle formula is 360° ÷ n, where n is the number of sides.

Definition: The interior angle of a regular polygon formula is (n2)×180°(n-2) × 180° ÷ n.

Lastly, it notes that for any polygon, the sum of an interior angle and an exterior angle at the same vertex is always 180°.

This comprehensive guide serves as an excellent resource for students studying geometry, providing essential formulas and concepts for understanding angle relationships in various shapes.

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Paul T

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Stefan S

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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