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0580/32 May/Jun 2024, Question 5: Angles in a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Use parallel-line, triangle and circle angle facts from the diagrams to name angles, justify values, and calculate y, angles at a tangent, and a regular 15-sided polygon's interior angle.

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

Part (ai) · 1 mark

State the mathematical term for the angle of 125° formed where a transversal meets parallel lines.

  1. 1125° is between 90° and 180°
  2. 2Obtuse

AnswerObtuse

Part (aii) · 1 mark

State the geometrical reason that makes x equal to 125.

  1. 1The 125° angle and x° lie on opposite sides of the transversal between the parallel lines
  2. 2Alternate angles are equal

AnswerAlternate angles

Part (b) · 3 marks

Calculate y from the three straight lines and list the angle properties used.

  1. 1The angle inside the triangle at the lower left = 58° (vertically opposite angles are equal)
  2. 2y = 180 − 58 − 70
  3. 3y = 52 (angles in a triangle add to 180°)

Answery = 52; opposite angles are equal, angles in a triangle add to 180

Part (ci) · 1 mark

Name the line CDE that touches the circle at D.

  1. 1CDE touches the circle at one point D
  2. 2It is a tangent

AnswerTangent

Part (cii) · 2 marks

Calculate angle ODB using the radius and diameter shown.

  1. 1OD = OB (radii), so triangle ODB is isosceles
  2. 2Angle ODB = (180 − 74) ÷ 2
  3. 3= 53°

Answer53

Part (ciii) · 2 marks

Calculate angle BDE and state the geometrical reason for it.

  1. 1Angle ODE = 90° (tangent meets radius at 90°)
  2. 2Angle BDE = 90 − 53
  3. 3= 37°

Answer37; angle between tangent and radius = 90°

Part (d) · 2 marks

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

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

Answer156

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

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Also searched as: 0580/32/M/J/24 · 0580_s24_qp_32 · 0580 s24 32 · question 5.
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