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0580/31 May/Jun 2022, Question 2: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

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The question, in short

Answer geometry questions on polygon sides, triangle types and angle measurement, pentagon interior angle, parallelogram angles, and triangle angles in ratio 3 : 5 : 7.

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

Part (a) · 1 mark

State how many sides a hexagon has.

  1. 1A hexagon has 6 sides

Answer6

Part (bi) · 1 mark

Give the mathematical name for a triangle with AB = AC.

  1. 1Two equal sides (AB = AC), so it is isosceles

AnswerIsosceles

Part (bii) · 1 mark

Measure angle CAB from the diagram.

  1. 1Measure with a protractor: angle CAB = 124°

Answer124 (accept 122 to 126)

Part (biii) · 1 mark

Given angle CAB = 124°, name this type of angle.

  1. 1124° is between 90° and 180°, so angle CAB is obtuse

AnswerObtuse

Part (c) · 2 marks

Show that a regular pentagon's interior angle is 108°.

  1. 1Exterior angle = 360 ÷ 5 = 72°
  2. 2Interior angle = 180 − 360/5 = 180 − 72 = 108°

Answer180 − 360/5 = 108 or ((5 − 2) × 180)/5 = 108

Part (d) · 2 marks

In parallelogram ABCD with reflex angle at D equal to 248°, find angle DCB.

  1. 1Angle ADC = 360 − 248 = 112°
  2. 2Co-interior angles add to 180°: angle DCB = 180 − 112
  3. 3= 68°

Answer68

Part (e) · 3 marks

Triangle angles are in ratio 3 : 5 : 7; find the largest angle.

  1. 13 + 5 + 7 = 15 parts; 180 ÷ 15 = 12° per part
  2. 2Largest angle = 7 × 12
  3. 3= 84°

Answer84

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 2.
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