Lemmara logoLemmaraWorked solution

0580/32 Feb/Mar 2022, Question 2: Angles in a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Find the interior angle of a regular pentagon, then use a diagram of three congruent regular pentagons and a triangle to work out angles x and y and their ratio.

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

Part (a) · 2 marks

Work out the size of one interior angle in a regular pentagon.

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

Answer108

Part (bi) · 2 marks

Using the pentagons meeting at a point, find x and state a geometrical reason.

  1. 1x = 360 − 3 × 108
  2. 2x = 36, because angles at a point add to 360°

Answer36; angles at a point add to 360

Part (bii) · 3 marks

Given x = 36, calculate y and give a geometrical reason for it.

  1. 1Interior angle of a regular pentagon = 540 ÷ 5 = 108°
  2. 2Angles at a point: x = 360 − 3 × 108 = 36
  3. 3The triangle is isosceles: two sides are equal pentagon sides
  4. 4Base angles are equal and angles in a triangle add to 180°
  5. 5y = (180 − 36) ÷ 2 = 72

Answer72; angles in a triangle add to 180 or base angles of an isosceles triangle are equal

Part (biii) · 1 mark

Express the ratio x : y in its simplest form.

  1. 1x : y = 36 : 72
  2. 2= 1 : 2

Answer1 : 2

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

Practise more angles in a triangle questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on angles in a triangle

Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.