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Angles in Parallel Lines

discia.org 10 questions · 27 marks
Name Date
  1. Either paper 1 mark
    The diagram shows two parallel lines crossed by a straight line. Four angles are marked with letters. acdb Circle the pair of co-interior angles.
    a and b a and c a and d c and d
    Show answer
    a and d
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  2. Either paper 2 marks

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

    41°x
    (a)

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

    (b)

    Give a reason for your answer.

    Show answer
    (a) \(41^\circ\)
    (b) Corresponding angles are equal
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  3. Either paper 2 marks

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

    67°xPQ
    (a)

    Work out the size of the angle marked \(x\).

    (b)

    Explain your answer.

    Show answer
    (a) \(67^\circ\)
    (b) Alternate angles are equal
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  4. Either paper 2 marks

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

    50°x
    (a)

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

    (b)

    Explain your answer.

    Show answer
    (a) \(50^\circ\)
    (b) Vertically opposite angles are equal
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  5. Either paper 2 marks

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

    x57°
    (a)

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

    (b)

    Explain your answer.

    Show answer
    (a) \(123^\circ\)
    (b) Co-interior angles add up to 180 degrees
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  6. Either paper 4 marks

    The two horizontal lines in the diagram are parallel.

    72°px
    (a)

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

    (b)

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

    Show answer
    (a) \(p = 72^\circ\), because vertically opposite angles are equal
    (b) \(x = 108^\circ\), because co-interior angles add up to 180 degrees
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  7. Either paper 3 marks

    The two horizontal lines in the diagram are parallel.

    132°x

    Noah says:

    "\(x = 132^\circ\), because alternate angles are equal."

    Noah is wrong.

    (a)

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

    (b)

    Explain the mistake he has made.

    Show answer
    (a) \(48^\circ\)
    (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 \(x = 48^\circ\) and not \(132^\circ\).
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  8. Either paper 5 marks

    In the diagram, ACF and ADG are straight lines. CD is parallel to FG.

    ACFGD58°64°

    Show that triangle ACD is isosceles.

    You must give a reason for each stage of your working.

    Show answer
    Angle ACD = 64° (corresponding angles are equal). Angle ADC = 180 - 58 - 64 = 58° (angles in a triangle add up to 180°). Angle CAD = angle ADC = 58°, so two angles are equal and triangle ACD is isosceles (CA = CD).
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  9. Either paper 3 marks

    \(ABCD\) is a trapezium.

    \(AB\) is parallel to \(DC\).

    Triangle \(ACD\) is isosceles with \(AD = DC\).

    ABCD84°56°

    Angle \(ADC = 56^\circ\).

    Angle \(ABC = 84^\circ\).

    Calculate the size of angle \(ACB\).

    Give a reason for each stage of your working.

    Show answer
    \(34^\circ\)
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  10. Either paper 3 marks

    The arrows show that the two straight lines are parallel.

    111°x

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

    Give a reason for each step of your working.

    Show answer
    \(69^\circ\)
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discia.org Angles in Parallel Lines · sheet 1
Answers Angles in Parallel Lines · sheet 1
  1. a and d
  2. (a) \(41^\circ\)
    (b) Corresponding angles are equal
  3. (a) \(67^\circ\)
    (b) Alternate angles are equal
  4. (a) \(50^\circ\)
    (b) Vertically opposite angles are equal
  5. (a) \(123^\circ\)
    (b) Co-interior angles add up to 180 degrees
  6. (a) \(p = 72^\circ\), because vertically opposite angles are equal
    (b) \(x = 108^\circ\), because co-interior angles add up to 180 degrees
  7. (a) \(48^\circ\)
    (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 \(x = 48^\circ\) and not \(132^\circ\).
  8. Angle ACD = 64° (corresponding angles are equal). Angle ADC = 180 - 58 - 64 = 58° (angles in a triangle add up to 180°). Angle CAD = angle ADC = 58°, so two angles are equal and triangle ACD is isosceles (CA = CD).
  9. \(34^\circ\)
  10. \(69^\circ\)
discia.org Angles in Parallel Lines · sheet 1