Angles Notes and examples: past paper questions

Real questions on angles notes and examples

The newest 20 of 143 written questions. Open one to see it on the real paper.

1. 4024/12 · May/June 2026 · Q1a[1]

   1-mark question — its maths and diagrams are best seen on the paper.

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2. 4024/12 · May/June 2026 · Q5b[1]

   1-mark question — its maths and diagrams are best seen on the paper.

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3. 4024/12 · May/June 2026 · Q16a[3]

   3-mark “Show” question — its maths and diagrams are best seen on the paper.

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4. 4024/12 · May/June 2026 · Q16b(i)[2]

   2-mark “Calculate” question — its maths and diagrams are best seen on the paper.

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5. 4024/12 · May/June 2026 · Q16b(ii)[1]

   1-mark “Complete” question — its maths and diagrams are best seen on the paper.

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6. 4024/12 · May/June 2026 · Q17c[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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7. 4024/11 · October/November 2025 · Q4a[2]
   The diagram shows five straight lines. [Diagram: Two parallel sloping lines (indicated by single arrows) intersect three parallel horizontal lines (indicated by double arrows). The left sloping line intersects the top horizontal line forming an interior angle of $q^{\circ }$. The right sloping line intersects the top hori...See it on the paper →
8. 4024/11 · October/November 2025 · Q4b[2]
   4 The diagram shows five straight lines. [Diagram: Five straight lines. Three horizontal parallel lines (indicated by double arrows) and two sloping parallel lines (indicated by single arrows). The left sloping line intersects the top horizontal line, forming an interior angle of $q^{\circ }$ on the right side. The right...See it on the paper →
9. 4024/12 · October/November 2025 · Q3[4]
   [Diagram: A parallelogram $ABCD$ with a point $E$ on side $AB$. A line segment connects $D$ to $E$ and $E$ to $C$. The angle $EDC$ is marked as $x^{\circ }$. The angle $DEC$ is marked as $60^{\circ }$. The angle $ECB$ is marked as $40^{\circ }$. Tick marks indicate that length $EC$ is equal to length $BC$. The diagram is labele...See it on the paper →
10. 4024/21 · October/November 2025 · Q25b[3]
    25 The diagram shows a cuboid. [Diagram: A cuboid with vertices A, B, C, D on the top face and E, F, G, H on the bottom face. A is above E, B above F, C above G, D above H. A dashed line connects E to C. A dashed line connects F to D. The length EH is labelled 12. The length HG is labelled 10. The length GC is labelled...See it on the paper →
11. 4024/22 · October/November 2025 · Q9[3]
    [Diagram: A regular pentagon and a regular hexagon joined along one edge. The angle $x^{\circ }$ is marked at the vertex where the two shapes meet, outside the shapes.] The diagram shows a regular pentagon and a regular hexagon joined along one edge. Find the value of $x$.See it on the paper →
12. 4024/12 · May/June 2025 · Q4[3]

    3-mark “Find” question — its maths and diagrams are best seen on the paper.

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13. 4024/13 · May/June 2025 · Q3a[1]
    [Diagram: A straight line $AB$ with a point on it. A line segment extends from this point to the right. The angle between the upper part of line $AB$ (toward $A$) and this segment is marked $x^{\circ }$. The angle between the lower part of line $AB$ (toward $B$) and this segment is marked $37^{\circ }$. The diagram is labele...See it on the paper →
14. 4024/13 · May/June 2025 · Q13a[2]
    13 The diagram shows a trapezium with lengths in centimetres. [Diagram: A trapezium with a right angle at the bottom left. The top parallel side is labelled 6, the bottom parallel side is labelled 9, and the left vertical side is labelled 4. The right side is slanted. The text "NOT TO SCALE" is to the right of the diag...See it on the paper →
15. 4024/13 · May/June 2025 · Q13b[3]
    13 The diagram shows a trapezium with lengths in centimetres. [Diagram: A trapezium with a right angle at the bottom left. The top horizontal side is labelled 6. The left vertical side is labelled 4. The bottom horizontal side is labelled 9. The right side is a slanted line. The text "NOT TO SCALE" is to the right of t...See it on the paper →
16. 4024/22 · May/June 2025 · Q4[2]
    [Diagram: Three parallel horizontal lines intersected by two parallel transversal lines. The top horizontal line and the left transversal form an angle labeled $y^{\circ }$. The middle horizontal line and the right transversal form an angle labeled $128^{\circ }$. The bottom horizontal line and the right transversal form an...See it on the paper →
17. 4024/22 · May/June 2025 · Q8[2]
    8 Calculate the interior angle of a regular octagon.See it on the paper →
18. 4024/22 · May/June 2025 · Q14a[1]
    PQRS is a cyclic quadrilateral. APB is a tangent to the circle at $P$. Angle $SPB=37^{\circ }$ and angle $PSQ=85^{\circ }$. [Diagram: A circle with points $Q,R,S,P$ on its circumference forming a cyclic quadrilateral $PQRS$. A line $APB$ is tangent to the circle at $P$. The angle between the chord $PS$ and the tangent...See it on the paper →
19. 4024/22 · May/June 2025 · Q14b[2]
    [Diagram: A circle with a cyclic quadrilateral $PQRS$ inscribed in it. A line $APB$ is tangent to the circle at point $P$. The angle between the chord $PS$ and the tangent segment $PB$ is labelled $37^{\circ }$. The interior angle $\angle PSQ$ is labelled $85^{\circ }$. The text "NOT TO SCALE" is present.] $PQRS$ is a cycli...See it on the paper →
20. 4024/23 · May/June 2025 · Q17a[2]
    Points $B,D,E$ and $F$ lie on a circle. $AC$ is a tangent to the circle at $B$. Angle $BEF=50^{\circ }$ and $EF=BF$. (a) Find the value of $x$. Give a geometrical reason for your answer. [Diagram: A circle with points $E,F,B,D$ on its circumference. $EF$ and $BF$ are marked as equal length. Angle $BEF$ is marke...See it on the paper →

What examiners said

A high proportion of candidates were able to calculate the missing angle. The common error was to think the total sum of the exterior angles of the pentagon was 540° and to subtract the sum of the given angles from this. A few thought the total was 720°. Others gained a method mark for just making an arithmetic slip in adding.

— Examiner report, October/November 2023, 4024/11 Q10(a) (Cambridge)

Many answers were correct or followed through from part (a) correctly by using their answer subtracted from 180. Some candidates gave the same answer in both parts, even though it was clear from the diagram that one angle was acute and the other obtuse.

— Examiner report, October/November 2023, 4024/12 Q6(b) (Cambridge)

Many candidates measured the angle accurately. Some misinterpreted the meaning of angle ABC so measured all three angles in the triangle and gave their answer as 180°, the sum of these angles. Some candidates misread the scale on their protractor giving an answer greater than 90° when the angle can be seen to be acute.

— Examiner report, October/November 2023, 4024/12 Q14(a) (Cambridge)