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#118

Angles in polygons

Geometry · Grade 4–6

Strand: Geometry Substrand: Angles Sparx code: U427 Sparx levels: 1, 2, 3, 4, 5

Key steps (method)

  • Mark the given angles clearly on the diagram.
  • Use the correct angle facts (straight line 180°, around a point 360°, triangle 180°, parallel line rules, etc.).
  • Work step-by-step, stating the reason for each angle you find.
  • If algebraic, set up an equation using the angle rule then solve.
  • Check the size is sensible for the diagram.

Common mistakes

  • Using the wrong angle rule (e.g. confusing corresponding and alternate angles).
  • Not justifying steps — missing easy method marks.
  • Arithmetic/sign errors when solving the resulting equation.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Angles in polygons (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes