4MA1/1H Jun 2024, Question 24: Interior and Exterior Angles of Polygons
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
A polygon with n > 5 sides has interior angles in arithmetic progression, smallest 84° and common difference 4°. Find the sum of its interior angles, showing algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1Sum of the n angles: n/2 × (2 × 84 + (n − 1) × 4) = 2n² + 82n.
- 2Sum of interior angles is also 180(n − 2) = 180n − 360.
- 32n² + 82n = 180n − 360, so n² − 49n + 180 = 0.
- 4(n − 45)(n − 4) = 0 and n > 5, so n = 45.
- 5Sum = 180 × (45 − 2) = 7740
Answer7740
Stuck on a step? Read the free lesson: Interior and Exterior Angles of Polygons
Practise more interior and exterior angles of polygons questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on interior and exterior angles of polygons
Also searched as: 4MA1 1H June 2024 · 4MA1/1H · 4ma1 jun24 1h · question 24.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.