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4MA1/1FR Jun 2025, Question 7: Angles in a Quadrilateral

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

Two geometry problems: explain why vertically opposite angles give x = 58, then use quadrilateral GHIJ angles to test whether FGH is a straight line.

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

Part (a) · 1 mark

State the angle relationship between the two marked angles at the intersection E that justifies x = 58.

  1. 1x and 58° are opposite each other where two straight lines cross
  2. 2Vertically opposite angles are equal, so x = 58

AnswerVertically opposite angles are equal

Part (b) · 4 marks

Use the angles in quadrilateral GHIJ to find angle HGJ, then compare with 110° to test if FGH is straight.

  1. 1Angles in a quadrilateral add up to 360°
  2. 2Angle JGH = 360 − 163 − 90 − 47 = 60°
  3. 3Angle FGH = 110 + 60 = 170°
  4. 4Angles on a straight line add up to 180°
  5. 5170° ≠ 180°, so FGH is not a straight line

AnswerAngle FGH = 170°, not 180°, so FGH is not a straight line

Stuck on a step? Read the free lesson: Angles in a Quadrilateral

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