Lemmara logoLemmaraWorked solution

0580/22 Oct/Nov 2025, Question 6: Angles in a Quadrilateral

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Quadrilateral ABCD with E on CD, AE parallel to BC, EA = ED, angle BAE = 75° and angle BCD = 80°. Find three angles.

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

Part (a) · 1 mark

Find angle ABC.

  1. 1AE is parallel to BC, so angles ABC and BAE are co-interior
  2. 2Angle ABC = 180 − 75 = 105°

Answer105

Part (b) · 1 mark

Find angle AED.

  1. 1AE is parallel to BC, so angle AED = angle BCD (corresponding angles)
  2. 2Angle AED = 80°

Answer80

Part (c) · 2 marks

Find angle DAB.

  1. 1AE is parallel to BC, so angle AED = angle BCD = 80° (corresponding angles).
  2. 2EA = ED, so triangle AED is isosceles: angle EAD = angle EDA.
  3. 3Angle EAD = (180 − 80) ÷ 2 = 50°
  4. 4Angle DAB = 50 + 75 = 125°

Answer125

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

Practise more angles in a quadrilateral questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on angles in a quadrilateral

Also searched as: 0580/22/O/N/25 · 0580_w25_qp_22 · 0580 w25 22 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.