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4MA1/2HR Jun 2020, Question 16: Angles in the Same Segment

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

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The question, in short

For five points A, B, C, D, E on a circle with angle EAC = 40°, find angle EBC, justify it, and find angle EDC.

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

Part (ai) · 1 mark

State the size of angle EBC.

  1. 1Angle EAC = 40°
  2. 2Angle EBC = Angle EAC because they are angles in the same segment
  3. 3So angle EBC = 40°

Answer40

Part (aii) · 1 mark

Give the circle theorem that justifies the size of angle EBC.

  1. 1Angles subtended by the same arc EC at the circumference are equal
  2. 2Therefore, angle EAC = angle EBC

AnswerAngles in same segment (are equal)

Part (b) · 1 mark

Find the size of angle EDC.

  1. 1Angle EAC = 40°
  2. 2Angle EDC is opposite angle EAC in cyclic quadrilateral AECD
  3. 3Opposite angles in a cyclic quadrilateral sum to 180°
  4. 4So angle EDC = 180° − 40° = 140°

Answer140

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