IGCSE Polygons: Complete Guide for Cambridge IGCSE Mathematics

IGCSE polygons are essential geometry topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering polygon properties, interior and exterior angles, and regular polygons is essential for solving geometry problems.

This comprehensive IGCSE polygons guide covers everything you need to know, including sum of interior angles, each interior angle, exterior angles, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate interior and exterior angles, work with regular polygons, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Geometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Polygons Matter

IGCSE polygons are essential geometry topics. Here’s why they’re so important:

• High frequency topic: Polygon questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding geometric shapes
• Exam weight: Typically worth 4-7 marks per paper
• Real-world applications: Used in design, architecture, and construction
• Problem-solving skills: Develops geometric reasoning

Key insight from examiners: Students often confuse interior and exterior angles or make errors with the formulas. This guide will help you master these systematically.

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Understanding Polygons

A polygon is a closed shape with straight sides.

Regular polygon: All sides and angles are equal Irregular polygon: Sides and/or angles are not all equal

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Sum of Interior Angles

Formula: Sum = (n - 2) × 180° where n = number of sides

Example 1: Find the sum of interior angles in an octagon.

Solution: n = 8 Sum = (8 - 2) × 180° = 6 × 180° = 1080°

Answer: 1080°

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Each Interior Angle (Regular Polygon)

Formula: Each angle = (n - 2) × 180° / n

Example 2: Find each interior angle of a regular hexagon.

Solution: n = 6 Each angle = (6 - 2) × 180° / 6 = 4 × 180° / 6 = 120°

Answer: 120°

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Exterior Angles

Sum of exterior angles = 360° (for any polygon)

Each exterior angle (regular polygon) = 360° / n

Example 3: Find each exterior angle of a regular pentagon.

Solution: n = 5 Each exterior angle = 360° / 5 = 72°

Answer: 72°

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Relationship Between Interior and Exterior Angles

Interior angle + Exterior angle = 180°

Example 4: A regular polygon has exterior angle 45°. Find the interior angle.

Solution: Interior angle = 180° - 45° = 135°

Answer: 135°

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Finding Number of Sides

Example 5: A regular polygon has interior angle 150°. How many sides?

Solution: Exterior angle = 180° - 150° = 30° n = 360° / 30° = 12 sides

Answer: 12 sides

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Common Examiner Traps

• Formula errors - Remember: Sum = (n-2)×180°, Each = (n-2)×180°/n
• Confusing interior/exterior - Interior + Exterior = 180°
• Regular vs irregular - Formulas apply to regular polygons for “each angle”

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Practice Questions

Question 1

Find the sum of interior angles in a decagon (10 sides).

Solution: Sum = (10 - 2) × 180° = 8 × 180° = 1440°

Answer: 1440°

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Tutopiya Advantage: Personalised IGCSE Polygons Coaching

• Live whiteboard walkthroughs of polygon problems
• Exam-docket homework packs mirroring CAIE specimen papers
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• Flexible slots with ex-Cambridge markers for last-mile polishing

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Frequently Asked Questions About IGCSE Polygons

What is a polygon?

A polygon is a closed shape with straight sides.

What is the sum of interior angles?

Sum = (n - 2) × 180° where n is the number of sides.

What is the sum of exterior angles?

Sum of exterior angles = 360° for any polygon.

How do I find the number of sides?

Use: n = 360° / (exterior angle) for regular polygons.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Angle Theorems: Complete Guide - Master angle theorems
• IGCSE Circle Theorems: Complete Guide - Master circle theorems
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Polygons with Tutopiya

Ready to excel in IGCSE polygons? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master polygons and achieve your target grade.

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