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Angles and polygons: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on G3 Angles and polygons, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q11

    June 2025 · Paper 2H

    3 marksG3 Angles and polygons
    The whole paper ↗
    June 2025 Paper 2H, question 11: A straight line is drawn across a regular octagon. Work out the size of angle x. Not drawn accurately x = °

  2. Q15

    November 2024 · Paper 2H

    4 marksG3 Angles and polygonsA21 Forming and solving equations
    The whole paper ↗
    November 2024 Paper 2H, question 15: AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ Work out the value of x. Not drawn accurately x = °

  3. Q17

    June 2024 · Paper 2H

    4 marksA21 Forming and solving equationsG3 Angles and polygons
    The whole paper ↗
    June 2024 Paper 2H, question 17: AB is a straight line. Both angles are given in degrees. By working out the value of x, work out the ratio smaller angle : larger angle Not drawn accurately Ans

  4. Q14

    June 2024 · Paper 3H

    3 marksG3 Angles and polygonsR4 Ratio notation
    The whole paper ↗
    June 2024 Paper 3H, question 14: Not drawn accurately b = 45° and a : b = 7 : 3 and x : y = 4 : 1 Show that a : y = 5 : 2

  5. Q2

    November 2023 · Paper 1H

    1 markG3 Angles and polygons
    The whole paper ↗
    November 2023 Paper 1H, question 2: Work out the size of an exterior angle of a regular hexagon. Answer °

  6. Q12

    November 2023 · Paper 3H

    3 marksG3 Angles and polygons
    The whole paper ↗
    November 2023 Paper 3H, question 12: AF, BC, DE and DF are straight lines. BC and DE are parallel. p is three times r. Work out the size of angle p. Not drawn accurately p = °

  7. Q4

    June 2023 · Paper 1H

    3 marksG3 Angles and polygons
    The whole paper ↗
    June 2023 Paper 1H, question 4: ABC, BD and BE are straight lines. angle EBD = 5 × angle ABE angle DBC = 3 × angle ABE Work out the size of angle EBD. Not drawn accurately Answer °

  8. Q6

    June 2023 · Paper 2H

    3 marksG3 Angles and polygons
    The whole paper ↗
    June 2023 Paper 2H, question 6: (a) Part of a regular polygon is shown. Assume that the polygon is an octagon. Work out the size of an exterior angle. Not drawn accurately Answer ° 6 (b) In fa

  9. Q28

    June 2022 · Paper 2H

    4 marksG6 Geometric proofG3 Angles and polygons
    The whole paper ↗
    June 2022 Paper 2H, question 28: AB, BC and CD are sides of a regular 12-sided polygon. CDMN is a square. Prove that points A, B and N lie on a straight line.

  10. Q6

    November 2021 · Paper 2H

    3 marksG3 Angles and polygons
    The whole paper ↗
    November 2021 Paper 2H, question 6: Lines A, B, C, D and E intersect as shown. Lines A and B are parallel. Work out the size of angle x. Not drawn accurately Answer degrees

  11. Q12

    November 2021 · Paper 3H

    2 marksG3 Angles and polygons
    The whole paper ↗
    November 2021 Paper 3H, question 12: Part of a regular polygon with 15 sides is shown. Work out the size of an interior angle. Not drawn accurately Answer degrees

  12. Q20

    November 2020 · Paper 2H

    3 marksG3 Angles and polygons
    The whole paper ↗
    November 2020 Paper 2H, question 20: AB, BC, CD and DE are four of the sides of a regular decagon. Not drawn accurately Work out the size of angle w. Answer degrees

  13. Q9

    November 2019 · Paper 2H

    3 marksG15 Measuring, scale drawings and bearingsG3 Angles and polygons
    The whole paper ↗
    November 2019 Paper 2H, question 9: J and K are ships. P is a port. J is due South of P. Angle JPK = 56° JP = KP Work out the bearing of J from K. Not drawn accurately Answer °

  14. Q14

    June 2019 · Paper 1H

    3 marksG3 Angles and polygonsR4 Ratio notation
    The whole paper ↗
    June 2019 Paper 1H, question 14: Here is a quadrilateral. a = 90° and a : b = 5 : 3 x : y = 1 : 3 Show that b = x Not drawn accurately

  15. Q7

    November 2018 · Paper 1H

    2 marksG3 Angles and polygons
    The whole paper ↗
    November 2018 Paper 1H, question 7: The sum of the angles in any quadrilateral is 360° For example, in a rectangle 4 × 90° = 360° Zak writes, 5 × 90° = 450° so the sum of the angles in any pentago

  16. Q4

    June 2018 · Paper 3H

    1 markG3 Angles and polygons
    The whole paper ↗
    June 2018 Paper 3H, question 4: What is the size of an exterior angle of a regular decagon? Circle your answer. 18° 36° 144° 162°

  17. Q14

    November 2017 · Paper 1H

    3 marksG3 Angles and polygons
    The whole paper ↗
    November 2017 Paper 1H, question 14: Two congruent regular polygons are joined together. Work out the number of sides on each polygon. Not drawn accurately Answer

  18. Q8

    November 2017 · Paper 3H

    4 marksG3 Angles and polygonsG4 Quadrilaterals
    The whole paper ↗
    November 2017 Paper 3H, question 8: ABCD is a parallelogram. AB = BP Work out the size of angle x. Not drawn accurately Answer degrees

  19. Q10

    June 2017 · Paper 3H

    7 marksG3 Angles and polygonsA21 Forming and solving equations
    The whole paper ↗
    June 2017 Paper 3H, question 10: AB, CD and EF are straight lines. Not drawn accurately 10 (a) Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y? Answe

  20. Q19

    June 2017 · Paper 3H

    4 marksG10 Circle theoremsG3 Angles and polygons
    The whole paper ↗
    June 2017 Paper 3H, question 19: A, B, C, D and E are points on a circle. BFD and AFC are straight lines. DC = DF Not drawn accurately Work out the size of angle x. You must show your working w
All 23 questions on Angles and polygons, as a list
  1. June 2025, Paper 2H, Q11 (3 marks): A straight line is drawn across a regular octagon. Work out the size of angle x. Not drawn accurately x = °
  2. November 2024, Paper 2H, Q15 (4 marks): AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ Work out the value of x. Not drawn accurately x = °
  3. June 2024, Paper 2H, Q17 (4 marks): AB is a straight line. Both angles are given in degrees. By working out the value of x, work out the ratio smaller angle : larger angle Not drawn accurately Ans
  4. June 2024, Paper 3H, Q14 (3 marks): Not drawn accurately b = 45° and a : b = 7 : 3 and x : y = 4 : 1 Show that a : y = 5 : 2
  5. November 2023, Paper 1H, Q2 (1 mark): Work out the size of an exterior angle of a regular hexagon. Answer °
  6. November 2023, Paper 3H, Q12 (3 marks): AF, BC, DE and DF are straight lines. BC and DE are parallel. p is three times r. Work out the size of angle p. Not drawn accurately p = °
  7. June 2023, Paper 1H, Q4 (3 marks): ABC, BD and BE are straight lines. angle EBD = 5 × angle ABE angle DBC = 3 × angle ABE Work out the size of angle EBD. Not drawn accurately Answer °
  8. June 2023, Paper 2H, Q6 (3 marks): (a) Part of a regular polygon is shown. Assume that the polygon is an octagon. Work out the size of an exterior angle. Not drawn accurately Answer ° 6 (b) In fa
  9. June 2022, Paper 2H, Q28 (4 marks): AB, BC and CD are sides of a regular 12-sided polygon. CDMN is a square. Prove that points A, B and N lie on a straight line.
  10. November 2021, Paper 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. Not drawn accurately Answer degrees
  11. November 2021, Paper 3H, Q12 (2 marks): Part of a regular polygon with 15 sides is shown. Work out the size of an interior angle. Not drawn accurately Answer degrees
  12. November 2020, Paper 2H, Q20 (3 marks): AB, BC, CD and DE are four of the sides of a regular decagon. Not drawn accurately Work out the size of angle w. Answer degrees
  13. November 2019, Paper 2H, Q9 (3 marks): J and K are ships. P is a port. J is due South of P. Angle JPK = 56° JP = KP Work out the bearing of J from K. Not drawn accurately Answer °
  14. June 2019, Paper 1H, Q14 (3 marks): Here is a quadrilateral. a = 90° and a : b = 5 : 3 x : y = 1 : 3 Show that b = x Not drawn accurately
  15. November 2018, Paper 1H, Q7 (2 marks): The sum of the angles in any quadrilateral is 360° For example, in a rectangle 4 × 90° = 360° Zak writes, 5 × 90° = 450° so the sum of the angles in any pentago
  16. June 2018, Paper 3H, Q4 (1 mark): What is the size of an exterior angle of a regular decagon? Circle your answer. 18° 36° 144° 162°
  17. November 2017, Paper 1H, Q14 (3 marks): Two congruent regular polygons are joined together. Work out the number of sides on each polygon. Not drawn accurately Answer
  18. November 2017, Paper 3H, Q8 (4 marks): ABCD is a parallelogram. AB = BP Work out the size of angle x. Not drawn accurately Answer degrees
  19. June 2017, Paper 3H, Q10 (7 marks): AB, CD and EF are straight lines. Not drawn accurately 10 (a) Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y? Answe
  20. June 2017, Paper 3H, Q19 (4 marks): A, B, C, D and E are points on a circle. BFD and AFC are straight lines. DC = DF Not drawn accurately Work out the size of angle x. You must show your working w
  21. Specimen, Paper 1H, Q16 (4 marks): AB, CD and YZ are straight lines. All angles are in degrees. Show that AB is parallel to CD. Not drawn accurately A B C D Y Z x + 25 2x + 35 5x 85
  22. Specimen, Paper 3H, Q9 (1 mark): The exterior angle of a regular polygon is 45° Circle the name of the regular polygon. pentagon hexagon octagon decagon
  23. Specimen, Paper 3H, Q10 (3 marks): ABC is a triangle with AB = AC BA is parallel to CD. Show that angle x = 30 Not drawn accurately 15° C B P A x D

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