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4MA1/1H Jun 2020, Question 16: Angle at the Centre

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Circle with centre O and points L, M, N, P on its circumference; angle MNP is 58°. Work out angle MLP with justification, then the reflex angle MOP.

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

Part (ai) · 1 mark

Work out the size of angle MLP.

  1. 1MLP and MNP are opposite angles of the cyclic quadrilateral MNPL
  2. 2Angle MLP = 180° − 58° = 122

Answer122

Part (aii) · 1 mark

State the circle theorem that justifies the value found in part (ai).

  1. 1Angle MLP and angle MNP are opposite angles in a cyclic quadrilateral
  2. 2They sum to 180°

AnswerOpposite angles in a cyclic quadrilateral sum to 180°

Part (b) · 2 marks

Work out the reflex angle MOP.

  1. 1Angle at the centre = 2 × angle at the circumference.
  2. 2Angle MOP = 2 × 58 = 116°
  3. 3Reflex angle MOP = 360 − 116 = 244

Answer244

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