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0580/33 May/Jun 2024, Question 5: Angles in Parallel Lines

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Answer six geometry items: measure and name an angle, identify alternate and corresponding angles, find a parallelogram angle, a circle angle, a regular polygon's side count, and a right-triangle angle.

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

Part (ai) · 1 mark

Measure angle k from the diagram.

  1. 1Measure the smaller angle between the lines, then k = 360° − that angle
  2. 2k = 326°

Answer326

Part (aii) · 1 mark

State the mathematical name for the type of angle k.

  1. 1Between 180° and 360°: reflex angle

Answerreflex

Part (b) · 2 marks

From the parallel-line diagram, name the angle alternate to x and the angle corresponding to x.

  1. 1Alternate angles lie on opposite sides of the transversal, between the parallel lines: c
  2. 2Corresponding angles are in the same position at each intersection: d

AnswerAlternate: c, Corresponding: d

Part (c) · 1 mark

In the parallelogram with a 42° angle, find y.

  1. 1Co-interior angles in a parallelogram add to 180°
  2. 2y = 180 − 42 = 138

Answer138

Part (d) · 2 marks

With A, B, C on a circle centre O and AC a diameter, angle BAC = 17°, find angle ACB.

  1. 1AC is a diameter, so angle ABC = 90° (angle in a semicircle)
  2. 2Angle ACB = 180 − 90 − 17 = 73°

Answer73

Part (e) · 2 marks

A regular polygon has interior angle 171°; work out its number of sides.

  1. 1Exterior angle = 180 − 171 = 9°
  2. 2Number of sides = 360 ÷ 9 = 40

Answer40

Part (f) · 2 marks

In the right-angled triangle with opposite side 7.4 cm and hypotenuse 18.5 cm, calculate x.

  1. 1sin x = 7.4/18.5 = 0.4
  2. 2x = sin⁻¹(0.4) = 23.57… ≈ 23.6

Answer23.6 or 23.57 to 23.58

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Also searched as: 0580/33/M/J/24 · 0580_s24_qp_33 · 0580 s24 33 · question 5.
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