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0580/12 Oct/Nov 2025, Question 12: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 5 marks

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The question, in short

A parallelogram diagram marks the top-left interior angle as (3x + 10)° and the bottom-left interior angle as (x − 30)°. Form an equation, solve for x, then work out the biggest angle.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 4 marks

Using the two marked angles, set up an equation and solve it to get x.

  1. 1Co-interior angles (adjacent angles of a parallelogram) add up to 180°
  2. 2x − 30 + 3x + 10 = 180
  3. 34x − 20 = 180
  4. 44x = 200
  5. 5x = 50

Answer50

Part (b) · 1 mark

Work out the size of the biggest angle in the parallelogram.

  1. 1Largest angle = 3x + 10
  2. 2= 3 × 50 + 10 = 160°

Answer160

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