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0580/31 Oct/Nov 2021, Question 4: Angles in a Quadrilateral

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 10 marks

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The question, in short

Use parallel-line angle facts to find a and b, a quadrilateral with AD extended to find x, and a circle with diameter AC and tangent DCE to find x and y.

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

Part (ai) · 1 mark

Find angle a using the two pairs of parallel lines shown.

  1. 1a and 48° are corresponding angles on parallel lines
  2. 2a = 48

Answer48

Part (aii) · 1 mark

Find angle b at the crossing of the right line and lower line.

  1. 1b and 48° are co-interior angles between parallel lines
  2. 2b = 180 − 48 = 132

Answer132

Part (b) · 2 marks

Quadrilateral ABCD has angles 72°, 119° and 63°; AD is extended to E. Find x, angle CDE.

  1. 1Angles in a quadrilateral add up to 360°.
  2. 2Angle ADC = 360 − 119 − 63 − 72 = 106°
  3. 3ADE is a straight line, so x = 180 − 106 = 74

Answer74

Part (ci) · 1 mark

Give the mathematical name of line BC in the circle.

  1. 1BC joins two points on the circle
  2. 2It is a chord

AnswerChord

Part (cii) · 1 mark

Explain why angle ABC equals 90° given AC is a diameter.

  1. 1AC is a diameter
  2. 2The angle in a semicircle is 90°

AnswerAngle in a semicircle = 90°

Part (ciii) · 2 marks

Find x, angle BOC, using angle BAC = 46°.

  1. 1OA = OB (radii), so angle OBA = 46°
  2. 2Angle BOA = 180 − 46 − 46 = 88
  3. 3x = 180 − 88 = 92

Answer92

Part (civ) · 2 marks

Find y, angle ADC, using the tangent DCE and straight line ABD.

  1. 1Tangent ⟂ radius, so angle ACD = 90°
  2. 2y = 180 − 90 − 46 = 44

Answer44

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Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 4.
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