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4MA1/2H Jun 2023, Question 14: Angle in a Semicircle

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

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The question, in short

Circle with centre O, ROP a diameter, and angle PRQ = 22°. Find angles RQP and PSQ, giving a reason for each.

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

Part (ai) · 1 mark

Find the size of angle RQP.

  1. 1Angle in a semicircle is 90°
  2. 2ROP is a diameter, so angle RQP = 90°

Answer90

Part (aii) · 1 mark

State the circle theorem that justifies the value of angle RQP.

  1. 1Angle subtended by the diameter at the circumference is 90°

AnswerAngle in a semicircle is 90°

Part (bi) · 1 mark

Find the size of angle PSQ.

  1. 1Angle PRQ = 22°
  2. 2Angles in the same segment are equal
  3. 3Angle PSQ = angle PRQ = 22°

Answer22

Part (bii) · 1 mark

State the circle theorem that justifies the value of angle PSQ.

  1. 1Angle PSQ and angle PRQ are subtended by the same arc PQ
  2. 2Therefore, they are equal

AnswerAngles in the same segment (are equal)

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