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4024/22 May/Jun 2020, Question 9: Angles in Parallel Lines

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

Use parallel lines and an isosceles triangle with LM = LN and angle GLM = 126° to find angle FMN, justifying each step; then use a circle with diameter BC and angles x and y to find four angles.

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

Part (a) · 4 marks

Find angle FMN using the parallel lines and LM = LN, giving a reason for every step.

  1. 1Angle MLN = 180 − 126 = 54° (angles on a straight line)
  2. 2Angle LNM = (180 − 54)/2 = 63° (base angles of isosceles triangle LMN, LM = LN)
  3. 3Angle FMN = angle LNM = 63° (alternate angles, EF parallel to GH)

Answer63

Part (bi) · 1 mark

Find angle DBC in terms of x and/or y.

  1. 1Angle DBC = 1/2 × angle DOC (angle at centre is twice angle at circumference)
  2. 2Angle DBC = y/2

Answery/2

Part (bii) · 1 mark

Find angle ABD in terms of x and/or y.

  1. 1Angle ABD = angle ACD (angles in the same segment)
  2. 2Angle ABD = x

Answerx

Part (biii) · 2 marks

Find angle AED in terms of x and/or y, showing reasoning.

  1. 1Angle BAC = 90° (angle in a semicircle)
  2. 2Angle AED = angle BAE + angle ABE (exterior angle of triangle ABE)
  3. 3Angle AED = 90 + x

Answer90 + x

Part (biv) · 1 mark

Find angle BDA in terms of x and/or y.

  1. 1Angle BDC = 90° (angle in a semicircle), so angle BCD = 90 − y/2
  2. 2Angle BCA = 90 − y/2 − x
  3. 3Angle BDA = angle BCA (angles in the same segment) = 90 − x − y/2

Answer90 − x − y/2

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Also searched as: 4024/22/M/J/20 · 4024_s20_qp_22 · 4024 s20 22 · question 9.
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