AAAarubi AcademyGCSE Maths Edexcel first
Join nowSign in
GCSE Maths / Edexcel

Angles in parallel lines

Identify corresponding, alternate and co-interior angles in parallel-line diagrams and use them to find missing angles.

Geometry and MeasuresFoundation and HigherGrades 4 to 6Focused skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Angles in parallel lines

Pearson Edexcel GCSE Maths geometry G4: apply angle facts for parallel lines and transversals.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Parallel lines stay the same distance apart and never meet. A transversal is a line that cuts across them.

When a transversal crosses two parallel lines, it creates 8 angles. Labelling them helps you see which angles match, which are opposite, and which add to 180 degrees.

Corresponding angles are equal. They are in matching positions on the two parallel lines.

Alternate angles are equal. They often look like a Z shape between the parallel lines. In the labelled 8-angle diagram there are two interior alternate pairs: 3 = 6 and 4 = 5.

Co-interior angles add to 180 degrees. They often look like a C shape inside the parallel lines. There are two co-interior pairs: 3 + 5 = 180 degrees and 4 + 6 = 180 degrees.

The hardest part is not the arithmetic, it is recognising which angle fact is being shown in the diagram.

For Edexcel marks, write the angle reason: corresponding, alternate or co-interior.

Key ruleCorresponding and alternate angles are equal; the two co-interior pairs add to 180 degrees.

Diagram guide

parallel lineparallel line12345678Vertically opposite pairs are equal at each crossing.Corresponding: 1=5, 2=6, 3=7, 4=8Alternate inside pairs: 3=6 and 4=5Co-interior pairs: 3+5=180 and 4+6=180
All 8 anglesStart by labelling the eight angles. Corresponding pairs are 1=5, 2=6, 3=7 and 4=8. Interior alternate pairs are 3=6 and 4=5. Co-interior pairs are 3+5=180 degrees and 4+6=180 degrees.
aaCorresponding angles are in the same position.Same position, same size: a = a
Corresponding anglesCorresponding angles are equal because they sit in the same position on each parallel line.
bbccThere are two alternate pairs inside the lines.Both pairs are equal: b = b and c = c.Two Z angle pairs: 3=6 and 4=5
Alternate anglesAlternate angles are equal. Inside the two parallel lines, there are two Z-angle pairs: 3=6 and 4=5.
efcdThere are two co-interior pairs inside the lines.Each same-side pair adds to 180: e+f=180 and c+d=180.Two C angle pairs: 3+5=180 and 4+6=180
Co-interior anglesCo-interior angles are inside the parallel lines on the same side of the transversal. There are two same-side pairs: 3+5=180 degrees and 4+6=180 degrees.

Worked examples

Corresponding angles

A corresponding angle to 72 degrees is labelled x. Find x.

aaCorresponding angles are in the same position.Same position, same size: a = a
Example: matching positionsThe marked angles are in the same position on the two parallel lines, so they are equal.
  1. Corresponding angles are equal on parallel lines.
  2. x = 72 degrees.

Answer: 72 degrees

Alternate angles

An alternate angle to 58 degrees is labelled y. Find y.

bbccThere are two alternate pairs inside the lines.Both pairs are equal: b = b and c = c.Two Z angle pairs: 3=6 and 4=5
Example: Z angle pairThere are two possible interior Z-angle pairs. The marked pair is one of them, so the two angles are equal.
  1. Alternate angles are equal.
  2. y = 58 degrees.

Answer: 58 degrees

Co-interior angles

A co-interior angle with 112 degrees is labelled z. Find z.

efcdThere are two co-interior pairs inside the lines.Each same-side pair adds to 180: e+f=180 and c+d=180.Two C angle pairs: 3+5=180 and 4+6=180
Example: same-side interior pairThere are two same-side interior pairs. The marked pair is one of them, so the two angles add to 180 degrees.
  1. Co-interior angles add to 180 degrees.
  2. z = 180 - 112.

Answer: 68 degrees

Common mistakes

  • Treating co-interior angles as equal instead of adding to 180 degrees.
  • Spotting a Z shape when the lines are not marked parallel.
  • Using the right fact but giving no reason.
  • Confusing corresponding and alternate angle positions.

Quick exercise

Try these before moving to the exam-style questions.

  1. A corresponding angle to 64 degrees is x. Find x.
    aaCorresponding angles are in the same position.Same position, same size: a = a
    Quick check: correspondingSame position on each parallel line means the angles are equal.
  2. An alternate angle to 78 degrees is y. Find y.
    bbccThere are two alternate pairs inside the lines.Both pairs are equal: b = b and c = c.Two Z angle pairs: 3=6 and 4=5
    Quick check: alternateChoose the marked Z-angle pair. There are two possible alternate pairs in the full diagram.
  3. A co-interior angle with 105 degrees is z. Find z.
    efcdThere are two co-interior pairs inside the lines.Each same-side pair adds to 180: e+f=180 and c+d=180.Two C angle pairs: 3+5=180 and 4+6=180
    Quick check: co-interiorChoose the marked same-side interior pair. There are two possible co-interior pairs.
  4. A co-interior angle with 43 degrees is a. Find a.
    efcdThere are two co-interior pairs inside the lines.Each same-side pair adds to 180: e+f=180 and c+d=180.Two C angle pairs: 3+5=180 and 4+6=180
    Quick check: subtract from 180Use 180 degrees minus the known angle in the chosen co-interior pair.
  5. An alternate angle to 121 degrees is b. Find b.
    bbccThere are two alternate pairs inside the lines.Both pairs are equal: b = b and c = c.Two Z angle pairs: 3=6 and 4=5
    Quick check: obtuse alternate angleAlternate angles stay equal even when the chosen pair is obtuse.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Two parallel lines are crossed by a transversal. An alternate angle to 74 degrees is labelled x. Work out x.

bbccThere are two alternate pairs inside the lines.Both pairs are equal: b = b and c = c.Two Z angle pairs: 3=6 and 4=5
Question diagram: alternate anglesThe marked pair is an alternate angle pair between two parallel lines.
parallel linesalternate anglesfoundation geometry
Standard exam styleFoundation and HigherNon-calculator3 marks

Two co-interior angles on parallel lines are 117 degrees and x. Work out x.

efcdThere are two co-interior pairs inside the lines.Each same-side pair adds to 180: e+f=180 and c+d=180.Two C angle pairs: 3+5=180 and 4+6=180
Question diagram: co-interior anglesThe marked angles are inside the parallel lines on the same side of the transversal.
co-interior anglesparallel linesmethod marks
ChallengeFoundation and HigherEither4 marks

An angle on a straight line is 42 degrees. The adjacent angle is corresponding to angle x on a parallel line. Work out x.

parallel lineparallel line12345678Vertically opposite pairs are equal at each crossing.Corresponding: 1=5, 2=6, 3=7, 4=8Alternate inside pairs: 3=6 and 4=5Co-interior pairs: 3+5=180 and 4+6=180
Question diagram: two angle factsFirst use angles on a straight line, then transfer the matching corresponding angle to the other parallel line.
parallel linesstraight linemulti-step angle