0580/13 Oct/Nov 2025, Question 10: Angles in Parallel Lines
Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Use the diagram of an isosceles triangle between two parallel lines, with apex angle 40°, to find x and y, giving a reason for y.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Find the value of x using the isosceles triangle and the parallel lines.
- 1Base angles of the isosceles triangle = (180 − 40) ÷ 2 = 70°
- 2x = 70 (alternate angles with a base angle, parallel lines)
Answer70
Part (b) · 2 marks
Find the value of y and state a geometrical reason for your answer.
- 1The triangle is isosceles, so its two base angles are equal
- 2Each base angle = (180 − 40) ÷ 2 = 70°
- 3y and the 70° base angle lie on a straight line
- 4y = 180 − 70 = 110, angles on a straight line add to 180
Answer110, angles on a straight line add to 180
Stuck on a step? Read the free lesson: Angles in Parallel Lines
Practise more angles in parallel lines questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on angles in parallel lines
Also searched as: 0580/13/O/N/25 · 0580_w25_qp_13 · 0580 w25 13 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.