Angles in parallel lines Quiz (Grade 4)

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Score: 0 / 10

Angles in parallel lines — Notes & Worked Examples Show / Hide

Explanation:

When a straight line (transversal) crosses a pair of parallel lines, three angle rules are formed. In exam questions that say “Give reasons for your answer”, you must use the exact mathematical names (never write “Z-angles”, “F-angles”, or “C-angles”):

• Alternate angles are equal (Z-shape) • Corresponding angles are equal (F-shape) • Co-interior (allied) angles add up to 180° (C-shape). Also remember: vertically opposite angles are equal.

Example 1: Find angles x and y, giving a reason for each.

x = 65° (angles on a straight line add up to 180°)

y = 65° (alternate angles are equal)

Example 2: Two co-interior angles between parallel lines are (3x + 10)° and (2x − 5)°. Find the value of x.

Solution:

Co-interior angles add up to 180°:

(3x + 10) + (2x − 5) = 180 → 5x + 5 = 180

5x = 175 → x = 175 ÷ 5 = 35

Answer: x = 35

One Page Guide (PDF) Angles in parallel lines Worksheets

Question 1

[2 marks]

Find the value of x
Give a reason for your answer

Worked Solution & Answer

Equation of a line: y = mx + c
Parallel lines have the same gradient (m).
x = 125° (Alternate angles)

Answer: x = 125° (Alternate angles)

Question 2

[2 marks]

Find the value of y
Give a reason for your answer

Worked Solution & Answer

Equation of a line: y = mx + c
Parallel lines have the same gradient (m).
y = 77° (Corresponding angles)

Answer: y = 77° (Corresponding angles)

Question 3 AQA Nov 2021 2H Q6

[3 marks]

Lines A, B, C, D and E intersect as shown.
Lines A and B are parallel.

Work out the size of angle x.

Answer degrees

Worked Solution & Answer

Angle between Line B and Line C = 110° - 52° = 58° M1
Since Lines A and B are parallel, alternate/interior angle in the triangle is 58° M1
Angles in triangle sum to 180°:
x = 180° - 58° - 49° = 73°. A1

Answer: Answer 73 degrees

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 AQA Nov 2021 2F Q16

[3 marks]

Work out
AB is parallel to CD.
FG is a straight line.
Work out the size of angle x.

AB is parallel to CD.
FG is a straight line.
Work out the size of angle x.

Answer degrees

Worked Solution & Answer

Angle between ray C and FG = 53° (corresponding to angle at AB) M1
Along the straight line CD: 53° + x + 48° = 180° M1
x = 180° - 53° - 48° = 79° A1

Answer: Answer 79 degrees

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 Eduqas Jun 2017 2F Q24

[3 marks]

The diagram shows parallel lines intersecting transversals.

Work out the sizes of angle x and angle y.

Worked Solution & Answer

1. Finding x: M1
Angle x and the angle 75° are alternate angles between the top two parallel lines cut by the transversal, so x = 75°.
2. Finding y:
• In the large triangle formed by the transversals and the bottom line:
The bottom-left interior angle is 100°, the bottom-right angle is 48° M1
Top vertex angle = 180° - 100° - 48° = 32°.
• In the triangle formed by the top vertex, the transversals, and the parallel line:
The top angle is 32°, and the right interior angle is 75°
Therefore, y = 180° - 32° - 75° = 73°. A1

Answer: x = 75°, y = 73°

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 Eduqas Nov 2022 2F Q15

[3 marks]

Find the value of x and the value of y.

Worked Solution & Answer

Co-interior angles sum to 180°: M1
3x + 126° = 180° ⇒ 3x = 54° ⇒ x = 18°. M1
2y + 152° = 180° ⇒ 2y = 28° ⇒ y = 14°. A1

Answer: x = 18, y = 14

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 OCR Jun 2023 2F Q18

[4 marks]

In the diagram, line AB is parallel to line ED.
The points A, C and D lie on a straight line.
The points B, C and E lie on a straight line.

Angle BCA = 45°, angle ABC = x° and angle CDE = y°.
The ratio x : y is 3 : 2.
Work out the value of x.

x =

Worked Solution & Answer

Alternate angles: angle CAB = angle CDE = y° M2
In triangle ABC: x + y + 45 = 180 ⇒ x + y = 135 M1
Since x : y = 3 : 2, x = (3/5) × 135 = 3 × 27 = 81. A1

Answer: x = 81

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 IGCSE Jan 2023 2F Q15

[4 marks]

The diagram shows two parallel lines AB and DEF

BEG is a straight line.
angle DEG = 73° angle EBC = 124° angle ABC = w°
Work out the value of w
Give reasons for each stage of your working.

w =

Worked Solution & Answer

Angle ABE = 73° (corresponding angles are equal) M3
Angles around point B sum to 360°, so w = 360 − (73 + 124) = 163. A1

Answer: w = 163

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 OCR Jun 2023 5H Q2

[5 marks]

The diagram shows two straight lines crossing a pair of parallel lines.

(a) Write down the value of a.
Give a reason for your answer. [2 marks]

(b) Work out the value of b. [3 marks]

b =

Worked Solution & Answer

(a)

a = 125 because corresponding angles on parallel lines are equal. M1 C1

Answer (a): a = 125 because corresponding angles are equal.

(b)

Interior angle at top-left of triangle = 180° − 125° = 55° M1
Interior angle at top-right of triangle = 75° (corresponding + vertically opposite). M1
b = 180° − 55° − 75° = 50°. A1

Answer (b): b = 50

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 Eduqas Nov 2019 2F Q12

[5 marks]

In the diagram, triangle ABC is isosceles.
AC and DE are parallel, BAĈ = 72° and ACD̂ = 37°.

(a) Find the size of angle BDÊ. [1 mark]

(b) Find the size of angle CDÊ. [1 mark]

(b) Write the mathematical name of quadrilateral ACED. [1 mark]

Worked Solution & Answer

(a)

Corresponding angle to BAĈ on parallel lines AC and DE: BDÊ = 72°. B1

Answer (a): 72° °

(b)

Alternate angle to ACD̂ between parallel lines AC and DE: CDÊ = 37°. B1

Answer (b): 37° °

(c)

Triangle ABC is isosceles with base AC: BCÂ = BAĈ = 72°. M1
ABĈ = 180° - 72° - 72° = 36°. A1

Answer (c): 36° °

(b)

Quadrilateral ACED has one pair of parallel sides (AC and DE), so it is a trapezium. B1

Answer (b): Trapezium

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 34 marks)

Angles in parallel lines Worksheets Next: Angles in polygons →

Grade 4 Quizzes

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction