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Grade 8–9 · Geometry of Straight Lines
Angles on Parallel Lines: The Complete Exam Guide
MEMORANDUM
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  / 37

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Two co-interior angles are (2x)° and (x + 30)°. Determine the value of x, and hence the size of each angle.
    (4)
    Co-interior angles on parallel lines add up to 180° (1)
    3x + 30 = 180 (1)
    x = 50 (1)
    The angles are 100° and 80° (1)    ✓✓✓✓ (4)
  2. 2
    Two corresponding angles are (5x − 18)° and (2x + 30)°. Determine the value of x, and hence the size of each angle.
    (4)
    Corresponding angles on parallel lines are equal (1)
    3x = 48 (1)
    x = 16 (1)
    The angles are 62° and 62° (1)    ✓✓✓✓ (4)
  3. 3
    Two co-interior angles are (3x − 20)° and (x + 40)°. Determine the value of x, and hence the size of each angle.
    (4)
    Co-interior angles on parallel lines add up to 180° (1)
    4x + 20 = 180 (1)
    x = 40 (1)
    The angles are 100° and 80° (1)    ✓✓✓✓ (4)
  4. 4
    In the diagram below, AB ∥ CD. Determine the size of x, giving a reason.
    (2)
    ABCD65°x
    x = 65°  (alt ∠s; AB ∥ CD)✓✓ (2)
  5. 5
    In the diagram below, AB ∥ CD. Determine the size of x. Give a reason for your statement.
    (2)
    ABCDx48°
    x = 48°  (corresp ∠s; AB ∥ CD)✓✓ (2)
  6. 6
    In the diagram below, AB ∥ CD. Write down the size of x and the reason for your answer.
    (2)
    ABCD130°x
    x = 180° − 130° = 50°  (co-int ∠s; AB ∥ CD)✓✓ (2)
  7. 7
    In the diagram below, AB ∥ CD. Determine, with a reason, the size of x.
    (2)
    ABCD90°x
    x = 180° − 90° = 90°  (co-int ∠s; AB ∥ CD)✓✓ (2)
  8. 8
    In the diagram below, POQ is a straight line. Determine the size of x.
    (2)
    PQRO72°x
    x = 180° − 72° = 108°  (∠s on a str line)✓✓ (2)
  9. 9
    Two straight lines intersect as shown in the diagram below. Determine the size of x.
    (2)
    115°x
    x = 115°  (vert opp ∠s)✓✓ (2)
  10. 10
    In the diagram below, AB ∥ CD. Determine the sizes of y and then x, giving reasons.
    (4)
    ABCD100°yx
    y = 100° (corresp ∠s; AB ∥ CD), then x = 180° − 100° = 80° (co-int ∠s; AB ∥ CD)✓✓✓✓ (4)
  11. 11
    In the diagram below, AB ∥ CD. Calculate the value of x.
    (3)
    ABCD(2x)°(x + 60)°
    3x + 60 = 180 → 3x = 120 → x = 40✓✓✓ (3)
  12. 12
    In the diagram below, AB ∥ CD. Solve for x.
    (3)
    ABCD(4x)°(x + 45)°
    4x = x + 45 → 3x = 45 → x = 15✓✓✓ (3)
  13. 13
    In the diagram below, AB ∥ CD. Determine the value of x.
    (3)
    ABCD(5x − 20)°(3x + 10)°
    5x − 20 = 3x + 10 → 2x = 30 → x = 15✓✓✓ (3)
TOTAL: 37 marks
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