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4MA1/2FR Jun 2023, Question 9: Angles in a Triangle

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 3 marks

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The question, in short

Quadrilateral ABCD has diagonal DB, with BC = CD = DB, a right angle at B in triangle ABD, and angle DAB = 32°. Find x, then y with a reason.

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

Part (a) · 1 mark

Using the equilateral triangle formed by BC, CD and DB, calculate the size of angle BCD, labelled x.

  1. 1BC = CD = DB, so triangle BCD is equilateral.
  2. 2Each angle in an equilateral triangle is 60°.
  3. 3x is angle BCD, so x = 60

Answer60

Part (bi) · 1 mark

Using triangle ABD with its right angle at B and the 32° angle at A, calculate angle ADB, labelled y.

  1. 1In triangle ABD, angle DBA = 90° and angle DAB = 32°
  2. 2Sum of angles in a triangle is 180°
  3. 3So angle ADB = 180° − 90° − 32° = 58°
  4. 4y is angle ADB, so y = 58

Answer58

Part (bii) · 1 mark

State the geometric property that justifies the value found for y in part (b)(i).

  1. 1The sum of the interior angles in any triangle is 180°
  2. 2This was used to find angle ADB in triangle ABD

Answerangles in a triangle add up to 180°

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

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