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Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

Edexcel IGCSE 4MA1 Quadrilaterals and Symmetry: Exam Questions and Answers

Quadrilaterals and Symmetry questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the worked example first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

Practise quadrilaterals and symmetry in Unit 5 →Quadrilaterals and Symmetry revision notes

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1 of 5

  1. Question 1 of 5
  2. Question 2 of 5
  3. Question 3 of 5
  4. Question 4 of 5
  5. Question 5 of 5

Start with one question on angles in polygons. Stuck? Take a hint. No sign-in needed.

Find the size of one exterior angle of a regular polygon with 12 sides.
Choose your answer · keys 1–4

What this topic covers

Quadrilaterals and Symmetry worked examples

Worked example 1: Angles in a kite

A kite has two equal angles of 110∘ and a third angle of 62∘. Find the fourth angle.

Kite with two equal angles of 110 degrees and a third angle of 62 degrees; the fourth angle is marked ?

Solution

3 steps · 1 to fill in
Tip: A kite has one pair of equal opposite angles.

Quadrilaterals and Symmetry exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 1 mark

Write down the order of rotational symmetry of a regular hexagon.

Show the answer and mark scheme
  • B1 6

Answer: 6

Question 2 · easy · 1 mark

A rhombus is not a square. How many lines of symmetry does it have?

Show the answer and mark scheme
  • B1 2

Answer: 2

Question 3 · easy · 1 mark

A quadrilateral has exactly one pair of parallel sides and exactly one line of symmetry. Write down the mathematical name of this quadrilateral.

Show the answer and mark scheme
  • B1 isosceles trapezium

Answer: Isosceles trapezium

Question 4 · medium · 2 marks

ABCD is a kite with AB = AD and CB = CD. Angle BAD = 110° and angle BCD = 50°. Work out the size of angle ABC.

Full worked solution Free, no sign-in

  • M1 (360 − 110 − 50) ÷ 2
  • A1 100°

Answer: 100°

Every question here has a full worked solution. See them all →

Question 5 · medium · 3 marks

In a parallelogram, two adjacent angles are (3x+10)∘ and (5x+10)∘. Find the value of x and the sizes of the two angles.

Show the answer and mark scheme
  • M1 3x + 10 + 5x + 10 = 180
  • A1 x = 20
  • A1 70° and 110°

Answer: x=20; 70° and 110°

Question 6 · medium · 3 marks

The diagonals of a rhombus have lengths 10 cm and 24 cm. Work out the length of one side of the rhombus.

Show the answer and mark scheme
  • B1 uses half-diagonals 5 and 12 with a right angle where the diagonals meet
  • M1 √(5² + 12²)
  • A1 13 cm

Answer: 13 cm

Question 7 · hard · 3 marks

A rhombus has sides of length 10 cm. One of its diagonals is 12 cm long. Work out the area of the rhombus.

Show the answer and mark scheme
  • M1 √(10² − 6²) = 8, so other diagonal 16
  • M1 ½ × 12 × 16 or 4 × ½ × 6 × 8
  • A1 96 cm²

Answer: 96 cm²

Question 8 · hard · 3 marks

ABCD is an isosceles trapezium with AB parallel to DC and AD = BC. Angle DAB = 68°. Work out the sizes of angles ABC, BCD and ADC, giving reasons.

Show the answer and mark scheme
  • B1 angle ABC = 68° (symmetry of isosceles trapezium)
  • M1 180 − 68 (co-interior angles between parallel lines)
  • A1 angle ADC = angle BCD = 112° with reasons

Answer: ABC = 68°, BCD = 112°, ADC = 112°

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

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Questions students ask

Which Edexcel IGCSE Maths papers test quadrilaterals and symmetry?

Either Higher tier paper, 1H or 2H, can test quadrilaterals and symmetry: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more quadrilaterals and symmetry questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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