Lemmara logoLemmaraWorked solution

0580/32 Feb/Mar 2025, Question 21: Interior and Exterior Angles of Polygons

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Show the pentagon angle sum is 540°, then use the five given angle expressions to form an equation and solve for x.

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

Part (a) · 1 mark

Show, by splitting the pentagon into triangles or otherwise, that its interior angles total 540°.

  1. 1A pentagon splits into 5 − 2 = 3 triangles
  2. 2(5 − 2) × 180 = 540°

Answer(5 − 2) × 180 or (180 − 360/5) × 5

Part (bi) · 2 marks

Add the five given angle expressions and simplify to get the pentagon's angle sum in terms of x.

  1. 1(3x − 25) + (3x − 5) + (x + 40) + 2x + (x + 35)
  2. 2x terms: 3 + 3 + 1 + 2 + 1 = 10; numbers: −25 − 5 + 40 + 35 = 45
  3. 3= 10x + 45

Answer10x + 45 or 5(2x + 9)

Part (bii) · 2 marks

Set the simplified angle sum equal to 540° and solve to find x.

  1. 110x + 45 = 540
  2. 210x = 495
  3. 3x = 49.5

Answer49.5

Stuck on a step? Read the free lesson: Interior and Exterior Angles of Polygons

Practise more interior and exterior angles of polygons 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 interior and exterior angles of polygons

Also searched as: 0580/32/F/M/25 · 0580_m25_qp_32 · 0580 m25 32 · question 21.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.