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Angles in Parallel Lines - Edexcel GCSE Higher Maths

Typically 3-5 marks per paper, usually inside a longer reasoning question · Spec 1MA1

When a straight line, the transversal, cuts across two parallel lines it creates eight angles and only two different sizes. Edexcel files this at spec reference G3, alongside angles at a point, angles at a point on a straight line, vertically opposite angles and the angle sum of a triangle. Three named relationships do the work: alternate angles are equal, corresponding angles are equal, and co-interior angles add up to 180∘180^\circ. That third pair also answers to allied or supplementary, and Edexcel accepts any of those names.

G3 is a crossover reference, so it is examined at both tiers, but the Higher versions look different. You will rarely meet a bare figure with one angle marked; the parallel-line step is one line in a longer chase that also passes through an isosceles triangle, a parallelogram or a trapezium, or it produces an equation in xx that you then solve. It can appear on any of the three papers and the calculator changes nothing, since the arithmetic is a subtraction from 180 or 360. What changes the mark total is the instruction attached: 'Give a reason for your answer' makes a 1-mark angle into a 2-mark question, and 'You must give reasons for each stage of your working' typically runs to 4-5 marks.

Finding the angle is the easy half. Mark schemes want the relationship named, with the word 'angles' present and the condition attached: 'alternate angles are equal', 'co-interior angles add up to 180∘180^\circ'. Edexcel now expects the proper names, so 'Z angles' and 'F angles' will not do, and 'because the lines are parallel', 'opposite angles' or 'they look the same' earn nothing on their own. Every figure is printed with 'Diagram NOT accurately drawn', so two lines are parallel only when the question says so, and a triangle is isosceles only when equal sides are given. Write each angle you find in three-letter notation, and put the reason on the same line as the calculation it justifies rather than in a paragraph at the end.

Worked example

ABC and DEF are parallel straight lines, labelled in the same direction so that A and D are at the same end. B lies on ABC. E and F lie on DEF, with the order along that line being D, E, F. The straight lines BE and BF are drawn. Angle ABE = 65∘65^\circ and angle EBF = 40∘40^\circ. Work out the size of angle BFE. Give a reason for each stage of your working.
[4 marks]
  1. BE is a transversal cutting the two parallel lines. Angle ABE sits between the lines on the A side of BE, and angle BEF sits between the lines on the F side, so they are alternate angles: angle BEF = 65∘65^\circ.
    M1: alternate angles used on the transversal BE to transfer 65 to the second parallel line
  2. B, E and F are the vertices of a triangle, so its three angles add to 180∘180^\circ: angle BFE = 180−65−40=75∘180 - 65 - 40 = 75^\circ.
    M1: angle sum of a triangle applied to their angle BEF
  3. Angle BFE = 75∘75^\circ.
    A1: 75, stated against the named angle rather than left as a bare number
  4. Reasons, written beside the lines they justify: alternate angles are equal; angles in a triangle add up to 180∘180^\circ.
    C1: the reasoning mark, needing the relationship named in full for each step, not just for the last one

Practice questions

These are original questions in Edexcel 1MA1 Higher style. There are no diagrams, so every figure is spelled out: which two lines are parallel, which line is the transversal, and where each labelled point sits along its line. Sketch each one first, then say to yourself which relationship you used, because on the real paper the reason carries a mark of its own.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Exam pace [3 marks]
    ABC and DEF are parallel straight lines, labelled in the same direction so that A and D are at the same end. The straight line BE crosses from B on ABC to E on DEF. Angle ABE = (3x+20)∘(3x + 20)^\circ and angle BEF = (5x−4)∘(5x - 4)^\circ. Work out the value of xx.
  2. Question 2 Exam pace [2 marks]
    A bookcase has two shelves that are parallel to each other. A straight diagonal support runs from the point B on the upper shelf down to the point E on the lower shelf. The points on the upper shelf are A, B, C in that order, and the points on the lower shelf are D, E, F in that order, with A and D at the same end of the bookcase. Angle EBC = 71∘71^\circ. Work out the size of angle BEF, in degrees.
  3. Question 3 Exam pace [2 marks]
    Two straight lines JK and LM are crossed by the straight line NP. NP crosses JK at X and crosses LM at Y. The two interior angles on the same side of NP are angle KXY = 88∘88^\circ and angle XYM = 94∘94^\circ. Which statement is correct?
    Answer options for question 3
  4. Question 4 Exam pace [3 marks]
    Three straight lines all pass through the point O, forming six angles around O. Going once round the point, the six angles are x∘x^\circ, 3x∘3x^\circ, 52∘52^\circ, x∘x^\circ, 3x∘3x^\circ and 52∘52^\circ in that order. Work out the value of xx.
  5. Question 5 Stretch [4 marks]
    ABCD is a trapezium with the vertices labelled in order round the shape. AD is parallel to BC, and AB = AD. The diagonal BD is drawn. Angle ADB = 37∘37^\circ. Work out the size of angle ABC, in degrees.
  6. Question 6 Stretch [4 marks]
    A picture frame is made from four straight pieces of wood. The top piece and the bottom piece are parallel to each other. The points on the top piece are A, X, B in that order, and the points on the bottom piece are C, Z, Y, D in that order, with A and C at the same end of the frame. Straight braces are fixed from X to Z and from X to Y. Angle AXZ = 27∘27^\circ and angle ZXY = 46∘46^\circ. Work out the sizes of angle XZY and angle XYZ, in degrees.

Common mistakes examiners see

  • Treating co-interior angles as equal. Given angle ABE = 118∘118^\circ, writing angle BED = 118∘118^\circ when the two close up a C shape and add to 180∘180^\circ, so the answer is 62∘62^\circ.

    Check where the two angles sit before you decide anything. Both between the parallel lines and both on the same side of the transversal means co-interior, so subtract from 180. On opposite sides of the transversal means alternate, so they are equal.

  • Getting the angle right and losing the reason mark by writing 'Z angles', 'F angles', 'opposite angles' or 'because the lines are parallel'.

    Learn three sentences and write one of them out in full: alternate angles are equal, corresponding angles are equal, co-interior angles add up to 180∘180^\circ. The word 'angles' has to appear, and so does the relationship.

  • Reading properties off the picture: calling two lines parallel because they look it, or a triangle isosceles because two sides are drawn the same length.

    Use only what is marked or stated: arrows for parallel lines, dashes for equal sides, a square for a right angle, or a sentence in the question. If none of those covers the step, find a route to the angle that does not need it.

  • Producing a correct chain of angles but naming none of them, so the working reads 64, 116, 32 and the examiner cannot tell which angle is which.

    Label every angle in three-letter notation as you find it, with the vertex in the middle: angle BEF = 64∘64^\circ. On a reasons question the examiner has to match each reason to a specific angle before the mark can be awarded.

  • Copying the given angle to the wrong angle of the pair, so an acute 62∘62^\circ is written where the obtuse 118∘118^\circ belongs.

    Decide whether the angle you want is acute or obtuse before you calculate. If the given angle is acute and the one you want is clearly obtuse, the pair is supplementary rather than equal, so take it from 180.

Frequently asked questions

Is angles in parallel lines on the Foundation paper as well as Higher?
Yes. G3 is a crossover reference on Edexcel 1MA1, so it is assessed at both tiers. The difference is the packaging: a Foundation question often gives the angle and asks for the reason, while a Higher question buries the parallel-line step inside a longer chase through a triangle or a quadrilateral, or turns it into an equation to solve.
How many marks are angles in parallel lines worth on Edexcel Higher?
A short one is usually 2 marks, one for the angle and one for the reason. A question that says 'you must give reasons for each stage of your working' is typically 4-5 marks, with the reasoning carrying its own marks separately from the arithmetic. Across a series expect it to contribute a few marks rather than a whole question of its own.
Can I write Z angles or F angles as my reason?
No. Edexcel expects the proper names: alternate angles, corresponding angles, co-interior angles. Co-interior angles may also be called allied or supplementary angles and both are accepted, but the letter-shape nicknames are not.
Are the angle facts printed on the Edexcel formulae sheet?
No. The Exam Aid sheet issued with each 1MA1 paper carries the area of a trapezium, volume of a prism, the circle formulae, the quadratic formula, Pythagoras' theorem and the trigonometric ratios, the sine and cosine rules, the area of a triangle, compound interest and two probability rules. Every angle fact in this topic is recall.

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