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0580/32 Oct/Nov 2022, Question 2: Angles in a Quadrilateral

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 14 marks

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The question, in short

Answer geometry questions on measuring an angle, using a scale drawing, parallel lines, triangle types, polygon angles and parallelogram angles.

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

Part (ai) · 1 mark

Use a protractor to find the size in degrees of the marked angle a.

  1. 1Measure with a protractor: a = 76°

Answer76 (accept 74 to 78)

Part (aii) · 1 mark

State the mathematical term for the kind of angle shown.

  1. 176° is less than 90°: acute

AnswerAcute

Part (bi) · 2 marks

Using the scale 1 cm to 8 km, calculate the real distance from B to C.

  1. 1BC measures 5.7 cm
  2. 2Distance = 5.7 × 8 = 45.6 km

Answer45.6 (accept 44 to 47.2)

Part (bii) · 1 mark

Measure the bearing in degrees of C as seen from B.

  1. 1Measure clockwise from North at B to BC: 124°

Answer124 (accept 122 to 126)

Part (c) · 2 marks

With two parallel lines cut by a transversal, work out the values of x and y.

  1. 1x = 180 − 47 = 133 (angles on a straight line)
  2. 2y = 47 (alternate angles)
  3. 3x = 133, y = 47

Answerx = 133, y = 47

Part (d) · 2 marks

Using the angles 119°, 31° and d°, show by calculation why the triangle must be scalene.

  1. 1d = 180 − 119 − 31 = 30
  2. 2Angles 119°, 31°, 30° are all different, so all sides are different: scalene

Answer30 and all three angles different

Part (e) · 2 marks

Calculate the size of a single interior angle in a regular polygon with 15 sides.

  1. 1Exterior angle = 360 ÷ 15 = 24°
  2. 2Interior angle = 180 − 24 = 156°

Answer156

Part (f) · 3 marks

Given one angle of 64° in a parallelogram, determine the sizes of the remaining three angles.

  1. 1Opposite angles are equal: 64°
  2. 2Co-interior angles: 180 − 64 = 116°
  3. 3Other three angles: 64°, 116°, 116°

Answer64, 116, 116

Stuck on a step? Read the free lesson: Angles in a Quadrilateral

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Also searched as: 0580/32/O/N/22 · 0580_w22_qp_32 · 0580 w22 32 · question 2.
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