EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Geometry & Measures · Foundation & Higher

Angle rules

Angles follow a set of rules based on their position. You must know these rules and be able to give reasons in geometry questions.

Revising angle rules the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Angle rules GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Angles on a straight line add up to 180°.
  • 2Angles around a point add up to 360°.
  • 3Vertically opposite angles are equal.
  • 4Angles in a triangle add up to 180°.
  • 5Angles in a quadrilateral add up to 360°.
  • 6Interior angles of a regular polygon: (n − 2) × 180° ÷ n.
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Formulas

Interior angle sum of polygon
(n − 2) × 180°

n = number of sides

Each interior angle (regular polygon)
(n − 2) × 180° ÷ n
Exterior angle (regular polygon)
360° ÷ n
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Worked examples

Example 1

Find the interior angle of a regular hexagon.

Working

  1. n = 6 sides
  2. Sum of interior angles = (6 − 2) × 180° = 720°
  3. Each angle = 720° ÷ 6 = 120°
Answer120°
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Common mistakes

✗Forgetting to give a reason when asked ("vertically opposite angles are equal", not just "they're equal").
✗Using the interior angle sum of a triangle (180°) for other polygons.
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Exam tips

✓Always write the geometric reason, not just the calculation — it's worth a mark.
✓Mark angles on the diagram as you find them to keep track.

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