AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 13

3 marks · Easy difficulty · Short Answer

Work out the value of x given two adjacent angles on a straight line, 74° and 2x.

Practise this question

Question

A geometric diagram showing straight line MN intersected by a line segment forming two adjacent angles on the straight line. One angle is labelled 74 degrees and the other adjacent angle is labelled 2x. A note states 'Not drawn accurately'. The question asks to work out the value of x, with an answer line followed by a degree symbol.

Mark scheme

Show the mark scheme Mark scheme for question 13 showing three marking steps: M1 for '180 - 74 or 106' or '2x + 74 = 180' (oe equation); M1dep for 'their 106 ÷ 2' or 'x = (180 - 74) ÷ 2'; A1 for the final answer of 53.

How to answer it

Angles on a Straight Line with Algebraic Terms

📋 What This Question Tests

This question assesses your ability to apply the fundamental geometric rule that angles on a straight line sum to 180°, set up a simple linear algebraic equation from a geometric diagram, and solve a two-step equation to find an unknown value.

Question 13 • 3 Marks

Finding the value of x along line MN

A line meeting a straight line forms two adjacent angles: 74° and 2x

💡 Key Knowledge

  • Angles on a straight line: Adjacent angles that make up a straight line always add up to 180°.
  • Algebraic representation: An angle labelled 2x means "2 multiplied by x".
  • Forming equations: Combine all adjacent angles to form the linear equation:
    2x + 74° = 180°

📐 Step-by-Step Solution

  1. Set up the equation:
    2x + 74 = 180
  2. Subtract 74 from both sides:
    2x = 180 − 74
    2x = 106°
    awarded M1 for finding 106° or writing the equation
  3. Divide by 2 to solve for x:
    x = 106 ÷ 2
    awarded M1 (dep) for dividing their remainder by 2
  4. Calculate final value:
    x = 53
    awarded A1 for the correct final answer

✅ Final Answer

Answer: 53

Note: The degree symbol (°) is already printed on the answer line in the exam paper. Writing just 53 gains full marks.

🧠 Exam Technique & Mark Scheme Tips

  • Method Marks (M): Always write down your subtraction ( 180 − 74 = 106 ). If you make an arithmetic error later when dividing, you still secure the first method mark!
  • Dependent Mark (M1dep): The second method mark depends on having attempted to find an angle on a straight line ( 180 − 74 ) first.
  • Quick Sanity Check: Substitute your answer back into the original diagram:
    2(53) + 74 = 106 + 74 = 180° . It checks out!

❌ Common Traps & Misconceptions

  • Stopping at 106: Forgetting that the angle is 2x , not x . Many students stop at 106 and lose the last 2 marks.
  • Using 360° or 90°: Confusing straight line angles (180°) with full turns (360°) or right angles (90°).
  • Measuring with a protractor: The question states "Not drawn accurately". Measuring the diagram directly will result in 0 marks.

Topics

Geometry and measures · Algebra · 3.2.3 Solving equations and inequalities · 3.4.1 Properties and constructions

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.