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0580/13 Oct/Nov 2023, Question 14: Angles in a Quadrilateral

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 3 marks

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The question, in short

Triangle ABC has angles 112° at B and 44° at C, with M the midpoint of AC. Rotating it 180° about M gives quadrilateral ABCD; name it and find angle BAD.

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

Part (a) · 1 mark

State the mathematical name of the quadrilateral ABCD formed by the triangle and its half-turn image.

  1. 1A 180° rotation about the midpoint of AC makes the diagonals bisect each other, so ABCD is a parallelogram

AnswerParallelogram

Part (b) · 2 marks

Calculate the size of angle BAD.

  1. 1A 180° turn about the midpoint of AC makes ABCD a parallelogram.
  2. 2Neighbouring angles in a parallelogram add to 180°.
  3. 3Angle BAD = 180 − 112 = 68°

Answer68

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Also searched as: 0580/13/O/N/23 · 0580_w23_qp_13 · 0580 w23 13 · question 14.
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