Angles: past paper questions

Where the questions come from

• Question 3May/June 2026, paper 11Structured2 marks

  Measure angle $a$.

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• Question 15Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  $ABC$ is a straight line and $ABD$ is an isosceles triangle. Work out the value of $x$.

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• Question 3Oct/Nov 2024, paper 11Structured2 marks

  Measure angle $x$.

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• Question 1Oct/Nov 2023, paper 11Structured1 mark

  Write down the mathematical name for this type of angle.

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• Question 10May/June 2026, paper 11Structured2 marksHas a diagram

  The diagram shows two straight lines intersecting two parallel lines. Complete each of these statements with the correct geometrical reason.

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• Question 12Oct/Nov 2025, paper 12Structured5 marks

  The diagram shows a parallelogram. Use the information in the diagram to write an equation and solve it to find the value of $x$.

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• Question 8Oct/Nov 2024, paper 11Structured2 marksHas a diagram

  The diagram shows a quadrilateral. Find the value of $y$.

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• Question 8Oct/Nov 2023, paper 11Structured2 marksHas a diagram

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

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• Question 17May/June 2026, paper 12Structured3 marks

  Two of the angles in a triangle are ${100}^{\circ }$ and ${30}^{\circ }$. Work out the size of the third angle.

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• Question 14Oct/Nov 2025, paper 12Structured3 marksHas a diagram

  The diagram shows a smaller triangle $DEF$ which has vertices on the sides of a larger triangle $ABC$. Find the value of $x$.

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• Question 24Oct/Nov 2024, paper 11Structured3 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 10Oct/Nov 2023, paper 11Structured2 marks

  $AB$ and $CD$ are parallel lines. Find the value of $x$.

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• Question 9May/June 2026, paper 13Structured5 marksHas a diagram

  $A$, $B$ and $C$ are points on the circumference of the circle, centre $O$. $DAE$ is a tangent to the circle at $A$. $DE$ is parallel to $BC$.

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• Question 22Oct/Nov 2025, paper 12Structured2 marks

  Work out the size of one interior angle of a regular hexagon.

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• Question 11Oct/Nov 2023, paper 12Structured2 marksHas a diagram

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

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• Question 11May/June 2026, paper 31Structured3 marksHas a diagram

  The scale diagram shows the positions of town $A$ and town $B$. The scale is $1\text{ cm}$ represents $15\text{ km}$. Measure the bearing of town $B$ from town $A$.

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• Question 24Oct/Nov 2025, paper 12Structured1 mark

  $B$ is a point on the circle, centre $O$. $ABC$ is a tangent to the circle at $B$ and angle $OAB={36}^{\circ }$. Work out the size of angle $AOB$.

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• Question 17Oct/Nov 2024, paper 12Structured4 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 15Oct/Nov 2023, paper 12Structured2 marks

  Calculate the interior angle of a regular 9-sided polygon.

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• Question 19May/June 2026, paper 31Structured3 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on the circumference of a circle with centre $O$. $AB=AD$ and angle $BDC={52}^{\circ }$. $BD$ is a diameter of the circle.

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• Question 9Oct/Nov 2024, paper 13Structured5 marksHas a diagram

  The scale drawing shows the positions of town $K$ and town $L$. The scale is 1 cm represents 10 km. Find the actual distance between town $K$ and town $L$.

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• Question 9Oct/Nov 2023, paper 13Structured2 marksHas a diagram

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

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• Question 23May/June 2026, paper 31Structured2 marks

  Calculate the interior angle of a regular pentagon.

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• Question 10Oct/Nov 2025, paper 13Structured4 marksHas a diagram

  The diagram shows an isosceles triangle between a pair of parallel lines. Find the value of $x$.

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• Question 11Oct/Nov 2024, paper 13Structured4 marksHas a diagram

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

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• Question 14Oct/Nov 2023, paper 13Structured3 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 8May/June 2026, paper 32Structured2 marks

  The scale drawing shows the position of a town, $T$. The scale is 1 centimetre represents 20 kilometres. A village, $V$, is 94 km from $T$ on a bearing of ${112}^{\circ }$.

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• Question 19Oct/Nov 2025, paper 13Structured2 marks

  Find the number of sides of a regular polygon with interior angle 160°.

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• Question 15Oct/Nov 2024, paper 13Structured2 marks

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

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• Question 2Oct/Nov 2023, paper 31Structured10 marksHas a diagram

  The diagram shows a circle. The diameter of this circle is $168\text{ mm}$. Write down the radius of this circle.

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