Angles: past paper questions

Where the questions come from

• Question 7May/June 2026, paper 21Structured2 marks

  The diagram shows the positions of three ships $P$, $Q$ and $R$. Ship $Q$ is $40\text{ km}$ due east of ship $R$. Ship $P$ is $40\text{ km}$ due north of ship $Q$.

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• Question 2Oct/Nov 2025, paper 21Structured3 marksHas a diagram

  In the diagram, $AC=BC$. Work out angle $CAB$.

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• Question 6Oct/Nov 2024, paper 21Structured3 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$ and a quadrilateral $AEDC$. Find the value of $x$

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• Question 1Oct/Nov 2023, paper 21Structured2 marksHas a diagram

  The diagram shows an isosceles triangle. Find the value of $x$.

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• Question 11May/June 2026, paper 22Structured2 marks

  Find the number of sides of a regular polygon with interior angle ${140}^{\circ }$.

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• Question 3Oct/Nov 2025, paper 21Structured2 marks

  Find the interior angle of a regular 20-sided polygon.

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• Question 9Oct/Nov 2024, paper 21Structured3 marks

  The diagram shows part of a regular polygon. The interior angle of the polygon is ${132}^{\circ }$ larger than the exterior angle. Calculate the number of sides of this polygon.

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• Question 5Oct/Nov 2023, paper 22Structured2 marksHas a diagram

  The diagram shows two intersecting straight lines crossing two parallel lines. Find the value of $x$.

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• Question 7May/June 2026, paper 23Structured3 marksHas a diagram

  The diagram shows the position of two towns, $A$ and $B$. The scale is $1\text{ cm}$ represents $2\text{ km}$. Work out the actual distance between $A$ and $B$.

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• Question 6Oct/Nov 2025, paper 22Structured4 marksHas a diagram

  ABCD is a quadrilateral. E lies on CD and AE is parallel to BC. EA = ED.

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• Question 5Oct/Nov 2023, paper 23Structured3 marksHas a diagram

  The diagram shows triangle $ABC$. $M$ is the midpoint of $AC$. Triangle $ABC$ is rotated ${180}^{\circ }$ about centre $M$.

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• Question 11May/June 2026, paper 23Structured2 marks

  The interior angle of a regular polygon is ${135}^{\circ }$. Find the number of sides of this regular polygon.

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• Question 16Oct/Nov 2025, paper 22Structured4 marks

  $AB$ and $BD$ are two sides of a regular 15-sided polygon. $AB$ and $BC$ are two sides of a regular $n$-sided polygon. Angle $DBC={14}^{\circ }$.

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• Question 8Oct/Nov 2024, paper 22Structured4 marksHas a diagram

  The diagram shows a parallelogram. Work out the size of the smallest interior angle of the parallelogram.

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• Question 4Oct/Nov 2023, paper 43Structured7 marksHas a diagram

  Find the size of one interior angle of a regular 10-sided polygon.

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• Question 1May/June 2026, paper 42Structured2 marksHas a diagram

  Triangle $ABC$ is isosceles with $AB=AC$. Find the value of $x$.

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• Question 6Oct/Nov 2024, paper 23Structured1 mark

  The diagram shows three lines meeting at a point. Find the value of $w$.

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• Question 1May/June 2023, paper 21Structured2 marksHas a diagram

  CDE is a straight line. Find angle ADE.

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• Question 8May/June 2026, paper 43Structured5 marksHas a diagram

  $AB$ and $CD$ are parallel lines. $AD$ and $BC$ are straight lines that intersect at $X$. Angle $ABX=y^{\circ }$.

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• Question 5Oct/Nov 2025, paper 23Structured2 marksHas a diagram

  The diagram shows a rectangle $ABCD$. $EFG$ is an equilateral triangle that touches the rectangle at $F$ and $G$. Find the value of $x$ and the value of $y$.

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• Question 9Oct/Nov 2024, paper 23Structured2 marks

  Find the size of an interior angle of a regular 15-sided polygon.

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• Question 3May/June 2023, paper 21Structured4 marksHas a diagram

  The diagram shows a straight line intersecting two parallel lines. Find the value of $a$ and the value of $b$, giving a geometrical reason for each answer.

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• Question 13Oct/Nov 2025, paper 23Structured4 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on the circumference of a circle with centre $O$. $ED$ and $EB$ are tangents to the circle. $AC$ is parallel to $EB$.

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• Question 4Oct/Nov 2024, paper 42Structured15 marksHas a diagram

  The angles of a quadrilateral are $w^{\circ }$, $x^{\circ }$, $y^{\circ }$ and $z^{\circ }$. The ratio $w:(x+y+z)=3:5$. Find the value of $w$.

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• Question 18May/June 2023, paper 21Structured4 marksHas a diagram

  The diagram shows the position of three towns, $U$, $V$ and $W$. $U$ is due west of $V$ and angle $UVW={125}^{\circ }$. Calculate the bearing of $U$ from $W$.

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• Question 3Oct/Nov 2025, paper 41Structured2 marksHas a diagram

  The diagram shows two parallel lines and a straight line. Find the value of $x$.

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• Question 6May/June 2024, paper 21Structured3 marksHas a diagram

  The diagram shows 5 kites that are congruent to kite $ABCD$. Each kite is joined to the next kite along one edge. Angle $DAB={40}^{\circ }$ and $DCE$ is a straight line.

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• Question 13May/June 2023, paper 22Structured2 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle. $AB$ is parallel to $DC$ and angle $ACD={32}^{\circ }$. Chords $AC$ and $DB$ intersect at $E$.

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• Question 15Oct/Nov 2025, paper 41Structured3 marksHas a diagram

  $A$, $B$ and $C$ lie on a circle, centre $O$. $TA$ and $TB$ are tangents to the circle at $A$ and $B$. Calculate angle $ATB$.

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• Question 15May/June 2024, paper 22Structured3 marksHas a diagram

  Three towns, $A$, $B$ and $C$, are equidistant from each other. The bearing of $C$ from $A$ is ${104}^{\circ }$. Calculate the bearing of $B$ from $C$.

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