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0580/31 Oct/Nov 2025, Question 9: Angles in a Quadrilateral

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 4 marks

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The question, in short

Identify an angle type from a diagram, explain why a stated triangle angle is wrong, and find x for a quadrilateral with a side extended.

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

Part (a) · 1 mark

Name the type of angle shown where two lines meet.

  1. 1The angle is more than 180°, so it is a reflex angle

Answerreflex

Part (b) · 1 mark

Give a geometrical reason why x = 34 is incorrect for triangle ABC with angles 102° and 54°.

  1. 1102 + 54 + 34 = 190, not 180
  2. 2Lily is wrong because angles in a triangle add to 180°

AnswerAngles in a triangle add to 180

Part (c) · 2 marks

Calculate x for quadrilateral ABCD, given angles 48°, 126°, 75° and straight line DCE.

  1. 1Angles in a quadrilateral add to 360°
  2. 2Angle BCD = 360 − (126 + 48 + 75) = 111°
  3. 3x = 180 − 111 = 69 (angles on a straight line)

Answer69

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

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Also searched as: 0580/31/O/N/25 · 0580_w25_qp_31 · 0580 w25 31 · question 9.
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