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4MA1/1F Jan 2020, Question 7: Angles in a Quadrilateral

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

Use the quadrilateral and triangle diagram with straight line DCB to find x and y, giving reasons for each result.

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

Part (ai) · 1 mark

Find the value of x using the angles in triangle ABC.

  1. 1In triangle ABC the angles are 17°, 125° and x°
  2. 2180 − 125 − 17 = 38, so x = 38

Answer38

Part (aii) · 1 mark

State the geometric reason for the value of x.

  1. 1The three angles of triangle ABC must add up to 180°

AnswerAngles in a triangle add up to 180°

Part (b) · 3 marks

Find y, giving a reason for each step of your working.

  1. 1Angle EAB is the right angle at A plus the 17°, so angle EAB = 90 + 17 = 107°
  2. 2In quadrilateral ABDE the angles are 107°, 38°, y° and 78°
  3. 3Angles in a quadrilateral add up to 360°
  4. 4107 + 38 + 78 = 223, so y = 360 − 223 = 137

Answer137

Stuck on a step? Read the free lesson: Angles in a Quadrilateral

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