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0580/31 May/Jun 2024, Question 5: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 13 marks

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The question, in short

Angle facts: name an angle type and use parallel lines and triangles with reasons, find a regular heptagon's interior angle, and solve for w, x and y from a regular pentagon's equal sides.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Name the type of angle that measures 105°.

  1. 1105° is between 90° and 180°
  2. 2Obtuse

Answerobtuse

Part (aii) · 2 marks

Find angle e using parallel lines and give the reason.

  1. 1e = 180 − 105 − 52
  2. 2e = 23
  3. 3Angles in a triangle add to 180°

Answere = 23, angles in a triangle add to 180

Part (aiii) · 2 marks

Find angle f and give the reason.

  1. 1Angle IFG and angle FGE are between parallel lines HI and EG
  2. 2f = 52
  3. 3Alternate angles are equal

Answerf = 52, alternate angles

Part (b) · 3 marks

Interior angle of a regular 7-sided polygon to 2 decimal places.

  1. 1Exterior angle = 360 ÷ 7 = 51.428…
  2. 2Interior angle = 180 − 51.428… = 128.571…
  3. 3= 128.57° (2 d.p.)

Answer128.57

Part (c) · 5 marks

Every side of the regular pentagon is 15 cm: set up equations and find w, x and y.

  1. 1All sides equal 15: 2w = 15, so w = 7.5
  2. 25(x + 7) = 15, so x + 7 = 3
  3. 3x = −4
  4. 4w + x + y = 15: 7.5 − 4 + y = 15
  5. 5y = 11.5

Answerw = 7.5, x = −4, y = 11.5

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