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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.

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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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