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0580/33 May/Jun 2021, Question 6: Angles in a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 9 marks

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The question, in short

Use circle and bearing geometry plus an isosceles triangle to determine unknown angles and a bearing.

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

Part (a) · 2 marks

Given diameter AB and angle BAC = 52°, work out angle ABC.

  1. 1Angle ACB = 90° (angle in a semicircle)
  2. 2Angle ABC = 180 − 90 − 52 = 38°

Answer38

Part (bi) · 2 marks

With bearings 042° and 146° from A to B and C, calculate angle BAC.

  1. 1Both bearings are measured clockwise from North at A.
  2. 2Angle BAC = 146 − 42 = 104°

Answer104

Part (bii) · 2 marks

Using the same two bearings, determine the bearing of A from B.

  1. 1Back bearing = 42 + 180
  2. 2Bearing of A from B = 222°

Answer222

Part (c) · 3 marks

In isosceles triangle ABC with AB = AC and exterior angle ACD = 117°, find x, where angle BAC = x°.

  1. 1Angle ACB = 180 − 117 = 63° (angles on a straight line)
  2. 2Angle ABC = 63° (isosceles triangle)
  3. 3x = 180 − 2 × 63 = 54

Answer54

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Also searched as: 0580/33/M/J/21 · 0580_s21_qp_33 · 0580 s21 33 · question 6.
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