Interior and Exterior Angles in Polygons - GCSE OCR Math Worksheet and Answers

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Crimsy

31/03/2023

Maths

Interior and Exterior angles (regular polygons)

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Maths

Geometry & measures

Angles

Interior and Exterior Angles in Polygons - GCSE OCR Math Worksheet and Answers

This document provides an overview of interior and exterior angles in regular polygons, focusing on formulas and examples for GCSE OCR math students. It covers key concepts and calculations related to polygon angles.

The document explains interior angles of regular polygons, including formulas and examples for various shapes.
It introduces the concept of exterior angles and provides a formula for calculating them.
Examples and practice questions are included to reinforce understanding of polygon angle calculations.

31/03/2023

POLYGONS interior angles)
Regular polygons
Regular means that all the angles and sides are the same
180
Triangle
900
Answer = 162
360
Square

Exterior Angles of Regular Polygons

This page focuses on the exterior angles of regular polygons, complementing the previous information on interior angles. It's an important topic for GCSE OCR math students studying polygon geometry.

The page introduces the formula for exterior angles: 180° - interior angle. This formula is crucial for understanding the relationship between interior and exterior angles in polygons.

Highlight: The sum of exterior angles in any polygon is always 360°.

The document provides a visual representation of exterior angles in a regular hexagon. This illustration helps students understand how exterior angles relate to the shape of the polygon.

Example: In a regular hexagon, each exterior angle measures 60° $360° ÷ 6$ .

The page also reinforces the connection between interior and exterior angles. It shows how the exterior angle is supplementary to the interior angle, meaning they add up to 180°.

Definition: Supplementary angles are two angles that add up to 180°.

This information is particularly useful for students working on exterior angles in regular polygons GCSE tips worksheets and preparing for exams.

The visual representation on this page can help students better understand concepts like the sum of exterior angles of a polygon and how it relates to the number of sides.

While there are no specific practice questions on this page, the information provided is essential for solving problems related to both interior and exterior angles of polygons, which are common in GCSE OCR math questions and worksheets.

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Interior and Exterior Angles in Polygons - GCSE OCR Math Worksheet and Answers

Crimsy

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Exterior Angles of Regular Polygons

This page focuses on the exterior angles of regular polygons, complementing the previous information on interior angles. It's an important topic for GCSE OCR math students studying polygon geometry.

The page introduces the formula for exterior angles: 180° - interior angle. This formula is crucial for understanding the relationship between interior and exterior angles in polygons.

Highlight: The sum of exterior angles in any polygon is always 360°.

The document provides a visual representation of exterior angles in a regular hexagon. This illustration helps students understand how exterior angles relate to the shape of the polygon.

Example: In a regular hexagon, each exterior angle measures 60° $360° ÷ 6$ .

The page also reinforces the connection between interior and exterior angles. It shows how the exterior angle is supplementary to the interior angle, meaning they add up to 180°.

Definition: Supplementary angles are two angles that add up to 180°.

This information is particularly useful for students working on exterior angles in regular polygons GCSE tips worksheets and preparing for exams.

The visual representation on this page can help students better understand concepts like the sum of exterior angles of a polygon and how it relates to the number of sides.

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

Interior Angles of Regular Polygons

This page focuses on the interior angles for regular polygons, a crucial topic in GCSE OCR math. It provides a comprehensive overview of how to calculate interior angles for various regular polygons.

Definition: Regular polygons are shapes where all angles and sides are equal.

The page introduces the formula for finding interior angles in polygons: $n-2$ × 180, where n is the number of sides. This formula is essential for solving problems related to polygon angles.

Example: For a triangle, the sum of interior angles is $3-2$ × 180 = 180°.

The document provides a visual representation of different regular polygons, from triangles to decagons, showing the sum of their interior angles. This helps students understand how the number of sides affects the total angle sum.

Highlight: The sum of interior angles increases as the number of sides in a polygon increases.

Several example questions are presented to demonstrate the application of the formula:

Finding the sum of interior angles for a heptagon $7 sides$ .
Calculating the size of each interior angle in a regular 20-sided polygon.
Determining the number of sides in a polygon given the sum of its interior angles.

These questions provide valuable practice for students preparing for GCSE OCR math worksheets and exams.

Vocabulary: Heptagon - a seven-sided polygon; Octagon - an eight-sided polygon; Nonagon - a nine-sided polygon; Decagon - a ten-sided polygon.

The page serves as an excellent resource for students studying angles in polygons, offering both theoretical knowledge and practical application through examples.

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Interior and Exterior Angles in Polygons - GCSE OCR Math Worksheet and Answers

Exterior Angles of Regular Polygons

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The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Interior and Exterior Angles in Polygons - GCSE OCR Math Worksheet and Answers

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