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Updated 12 Mar 2026

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2 pages

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

Crimsy

@crimsylit_fwgd

This document provides an overview of interior and exterior angles... Show more

# POLYGONS (interior angles

# Regular polygons

Regular means that all the angles and sides are the same

180

360

540

720

Triangle

Squ

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.

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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Updated 12 Mar 2026

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2 pages

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

Crimsy

@crimsylit_fwgd

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... Show more

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Exterior Angles of Regular Polygons

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

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°.

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.