Home   >  Worksheets   >  GCSE questions by topic   >  Angles in parallel lines

MathsLinks Logo Questions by topic

Last update: 05/11/2026

Give feedback : Buy me a coffee

Angles in parallel lines

Free Printable Angles in parallel lines PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 4)

Download free angles in parallel lines worksheets (PDF), GCSE maths past paper questions and worked solutions for Angles in parallel lines (4L). This is a Grade 4 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Maths4Everyone, Corbett Maths, Maths Made Easy, Dr Frost, Naiker Maths, Dr Austin, Cazoom Maths, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our angles in parallel lines revision notes and worked examples with diagrams, try real GCSE past paper angles in parallel lines questions with step-by-step solutions, or download a PDF of all angles in parallel lines worksheet links.

Free Angles in parallel lines PDF Worksheets & Answers

Grade 4 • Topic 4L
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
 Qs Ans
GCSE 9–1 practice booklet & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
MME worksheet & model answers
 Qs Ans
GCSE worksheet & solutions
 Qs Ans
Exam question booklet & solutions
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Cazoom Maths
Angles in parallel lines questions & answers
 Qs Ans
Practice questions & answers
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Online topic notes & examples
 Page
Interactive online lesson & practice
 Page
Self-marking online worksheet
 Page
Grade 4 topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction
GCSE Maths Grade 4 Revision Notes & Method

Guide to Angles in parallel lines: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

When a straight line (transversal) crosses a pair of parallel lines, three angle rules are formed. In exam questions that say “Give reasons for your answer”, you must use the exact mathematical names (never write “Z-angles”, “F-angles”, or “C-angles”):

• Alternate angles are equal (Z-shape)  • Corresponding angles are equal (F-shape)  • Co-interior (allied) angles add up to 180° (C-shape). Also remember: vertically opposite angles are equal.

Example 1: Find angles x and y, giving a reason for each.

115° x y
x = 65° (angles on a straight line add up to 180°)
y = 65° (alternate angles are equal)

Example 2: Two co-interior angles between parallel lines are (3x + 10)° and (2x − 5)°. Find the value of x.

Solution:

Co-interior angles add up to 180°:
(3x + 10) + (2x − 5) = 180 → 5x + 5 = 180
5x = 175 → x = 175 ÷ 5 = 35
Answer: x = 35
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Angles in parallel lines Questions & Answers

Past Paper Example 1 AQA Nov 2021 2H Q6 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Lines A, B, C, D and E intersect as shown.
Lines A and B are parallel.
Not drawnaccuratelyLine ALine BLine CLine D52°Line E110°49°x
Work out the size of angle x.
Worked Solution & Mark Scheme (3 marks)
Angle between Line B and Line C = 110° - 52° = 58° M1
Since Lines A and B are parallel, alternate/interior angle in the triangle is 58° M1
Angles in triangle sum to 180°:
x = 180° - 58° - 49° = 73°. A1
Answer: Answer 73 degrees
Past Paper Example 2 AQA Nov 2021 2F Q16 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Not drawnaccuratelyFGABCD53°E48°x
Work out
AB is parallel to CD.
FG is a straight line.
Work out the size of angle x.
AB is parallel to CD.
FG is a straight line.
Work out the size of angle x.
Worked Solution & Mark Scheme (3 marks)
Angle between ray C and FG = 53° (corresponding to angle at AB) M1
Along the straight line CD: 53° + x + 48° = 180° M1
x = 180° - 53° - 48° = 79° A1
Answer: Answer 79 degrees
Past Paper Example 3 Eduqas Jun 2017 2F Q24 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows parallel lines intersecting transversals.
x75°y100°48°Diagram not drawn to scale
Work out the sizes of angle x and angle y.
Worked Solution & Mark Scheme (3 marks)
1. Finding x: M1
Angle x and the angle 75° are alternate angles between the top two parallel lines cut by the transversal, so x = 75°.
2. Finding y:
• In the large triangle formed by the transversals and the bottom line:
The bottom-left interior angle is 100°, the bottom-right angle is 48° M1
Top vertex angle = 180° - 100° - 48° = 32°.
• In the triangle formed by the top vertex, the transversals, and the parallel line:
The top angle is 32°, and the right interior angle is 75°
Therefore, y = 180° - 32° - 75° = 73°. A1
Answer: x = 75°, y = 73°

← 4K Pythagoras theorem

Back to GCSE questions by topic

4M Angles in polygons →