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Geometry & MeasuresIntroduction

The Triangle Trick

Part of Angles in Polygons · GCSE GCSE Mathematics revision

This introduction covers The Triangle Trick within Angles in Polygons for GCSE Mathematics. Revise Angles in Polygons in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 10 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 10

Practice

12 questions

Recall

3 flashcards

The Triangle Trick

Here's a secret: EVERY polygon can be split into triangles by drawing lines from one vertex. A quadrilateral splits into 2 triangles, a pentagon into 3, a hexagon into 4... Since each triangle has 180°, you can calculate the interior angles of ANY polygon!

Visual: Polygon Interior Angles

Diagram showing how polygons split into triangles to calculate interior angles - triangle has 1 triangle (180°), square has 2 triangles (360°), pentagon has 3 triangles (540°), hexagon has 4 triangles (720°). Formula: (n-2) × 180°

Pattern: triangles = n − 2, each triangle = 180°

Keep building this topic

Read this section alongside the surrounding pages in Angles in Polygons. That gives you the full topic sequence instead of a single isolated revision point.

Essential FormulasCommon Polygon AnglesWorked Example 1: Interior Angle Sum

Practice Questions for Angles in Polygons

What is the sum of the interior angles of a hexagon?

  • A. 540°
  • B. 720°
  • C. 900°
  • D. 360°
1 markfoundation

Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.

2 markshigher

Quick Recall Flashcards

Interior Angle Sum
Sum = (n - 2) × 180° for n-sided polygon
Exterior Angle Sum
Always 360° for any polygon

12 questions on Angles in Polygons — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

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