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The Triangle Trick
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
Pattern: triangles = n − 2, each triangle = 180°
Now try it yourself
Quiz · Question 1 of 12
What is the sum of the interior angles of a hexagon?
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This topic in real past papers
Every real exam question we've found on angles in polygons, with a full worked answer.
AQA Paper 2
Three of the four sittings we have full papers for include this exact house-style question type, a tick-box asking how a changed assumption affects an earlier answer, and June 2023 uses it twice in the same paper.
Edexcel Paper 1
Two of the three sittings we have full papers for combine an angle-sum fact with a ratio between two unknown angles.