Discia GCSE Maths › Geometry & Measures › Angles in Parallel Lines

Angles in Parallel Lines worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 28 marks Sheet 1
Generate a different sheet
  1. 2 marks

    The arrows on the diagram show that the two straight lines are parallel.

    Two parallel lines crossed by a straight line. An angle of 137 degrees is marked above the lower line, on the right of the crossing line, and the angle marked x is in the matching position at the upper line.137°x
    (a)

    State the size of the angle marked \(x\).

    (b)

    Explain your answer.

  2. 2 marks

    A straight line crosses two parallel lines at \(P\) and at \(Q\).

    Two parallel lines crossed by a straight line at P on the lower line and Q on the upper line. An angle of 43 degrees is marked between the lines at P, and the angle x is marked between the lines at Q on the other side of the crossing line.43°xPQ
    (a)

    Calculate the size of the angle marked \(x\).

    (b)

    Give a reason for your answer.

  3. 2 marks

    The diagram shows two parallel lines crossed by a straight line.

    Two parallel lines crossed by a straight line. At the lower crossing an angle of 70 degrees is marked above the line and the angle x is marked directly opposite it, below the line.70°x
    (a)

    State the size of the angle marked \(x\).

    (b)

    Explain your answer.

  4. 2 marks

    The diagram shows two parallel lines crossed by a straight line.

    Two parallel lines crossed by a straight line. An angle of 66 degrees is marked between the lines at the upper crossing, and the angle x is marked between the lines at the lower crossing on the same side of the crossing line.x66°
    (a)

    Find the size of the angle marked \(x\).

    (b)

    Give a reason for your answer.

  5. 4 marks

    The two horizontal lines in the diagram are parallel.

    Two parallel lines crossed by a straight line. At the lower crossing an angle of 66 degrees is marked above the line and the angle p is marked opposite it below the line. At the upper crossing the angle x is marked between the two parallel lines.66°px
    (a)

    Write down the size of the angle marked \(p\), and give a reason for your answer.

    (b)

    Find the size of the angle marked \(x\), and give a reason for your answer.

  6. 3 marks

    The two horizontal lines in the diagram are parallel.

    Two parallel lines crossed by a straight line. An angle of 67 degrees is marked between the lines at the lower crossing and the angle x is marked between the lines at the upper crossing, on the same side of the crossing line.67°x

    Anya says:

    "\(x = 67^\circ\), because alternate angles are equal."

    Anya is wrong.

    (a)

    State the correct size of the angle marked \(x\).

    (b)

    Explain the mistake she has made.

  7. 3 marks

    The arrows show that the two straight lines are parallel.

    Two parallel lines crossed by a straight line. An angle of 63 degrees is marked below the lower line, on the left of the crossing line, and the angle x is marked between the two parallel lines at the upper crossing, on the right of the crossing line.63°x

    Calculate the size of the angle marked \(x\).

    Give a reason for each step of your working.

  8. 4 marks

    The two horizontal lines in the diagram are parallel. All angles are in degrees.

    Two parallel lines crossed by a straight line. The angle between the lines at the lower crossing is labelled 3x degrees and the angle between the lines at the upper crossing, on the same side of the crossing line, is labelled (2x + 105) degrees.3x°(2x + 105)°
    (a)

    Work out the value of \(x\).

    (b)

    Hence write down the size of the angle marked \(3x^\circ\).

  9. 4 marks

    The two horizontal lines in the diagram are parallel. Two straight lines cross them.

    Two parallel lines crossed by two different straight lines. On the left-hand crossing line an angle of 40 degrees is marked at the lower parallel line and the angle x is marked at the upper one. On the right-hand crossing line an angle of 61 degrees is marked at the upper parallel line and the angle q is marked at the lower one.40°xq61°
    (a)

    Find the size of the angle marked \(x\), and give a reason for your answer.

    (b)

    Find the size of the angle marked \(q\), and give a reason for your answer.

  10. 2 marks

    The arrows on the diagram show that the two straight lines are parallel.

    Two parallel lines crossed by a straight line. An angle of 137 degrees is marked above the lower line, on the right of the crossing line, and the angle marked x is in the matching position at the upper line.137°x
    (a)

    Write down the size of the angle marked \(x\).

    (b)

    Give a reason for your answer.

Answers

  1. (a) \(137^\circ\)
    (b) Corresponding angles are equal
  2. (a) \(43^\circ\)
    (b) Alternate angles are equal
  3. (a) \(70^\circ\)
    (b) Vertically opposite angles are equal
  4. (a) \(114^\circ\)
    (b) Co-interior angles add up to 180 degrees
  5. (a) \(p = 66^\circ\), because vertically opposite angles are equal
    (b) \(x = 114^\circ\), because co-interior angles add up to 180 degrees
  6. (a) \(113^\circ\)
    (b) They are co-interior angles, not alternate: both of them are on the same side of the crossing line. Co-interior angles add up to 180 degrees rather than being equal, so \(x = 113^\circ\) and not \(67^\circ\).
  7. \(117^\circ\)
  8. (a) \(x = 15\)
    (b) \(45^\circ\)
  9. (a) \(x = 40^\circ\), because alternate angles are equal
    (b) \(q = 119^\circ\), because co-interior angles add up to 180 degrees
  10. (a) \(137^\circ\)
    (b) Corresponding angles are equal

← All GCSE maths worksheets

{# Self-hosted. The public pages make no third-party request at all — see docs/PUBLIC_LAUNCH_HANDOFF.md before pointing this at a CDN again. #}