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0580/31 Oct/Nov 2024, Question 2: Angles in Parallel Lines

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

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The question, in short

Use parallel lines ABCD and EF with triangle BCG and given angles 38°, 69° to find x, y and z with reasons, then answer circle questions about tangent XY and chord SR.

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

Part (ai) · 2 marks

Find x using the 69° angle and parallel lines; state a geometrical reason.

  1. 1x = 38
  2. 2Alternate angles are equal (EF parallel to BD)

Answer38, Alternate angles

Part (aii) · 2 marks

Find y using the 38° angle and parallel lines; state a geometrical reason.

  1. 1y = 69
  2. 2Corresponding angles are equal (EF parallel to CD)

Answer69, Corresponding angles

Part (aiii) · 2 marks

Find z using the angles in triangle BCG.

  1. 1Angle BCG = 180 − 69 = 111° (angles on a straight line)
  2. 2z = 180 − 38 − 111 = 31 (angles in a triangle add to 180°)

Answer31

Part (bi) · 1 mark

Give the mathematical name of the line XY touching the circle at T.

  1. 1A line that touches the circle at one point is a tangent

AnswerTangent

Part (bii) · 1 mark

Give the mathematical name of the line SR joining two circle points.

  1. 1A line joining two points on the circle is a chord

AnswerChord

Part (biii) · 1 mark

Explain geometrically why triangle RST is not right-angled.

  1. 1Angle in a semicircle is 90° only when a side is a diameter
  2. 2None of the sides of the triangle is a diameter of the circle (none passes through O)

AnswerNone of the sides of the triangle is a diameter of the circle

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 2.
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