EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Interior Angles
Interior angles of a polygon · Angles and trigonometry · Lesson 2 of 7 · 10 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Work out the sum of the interior angles of a polygon with 9 sides.
Question 2 NON-CALCULATOR [2 marks]
Work out the size of each interior angle of a regular nonagon.
Question 3 NON-CALCULATOR [3 marks]
A hexagon has angles 2x, 2x, 3x, 3x, 4x and 4x, in degrees. Work out the value of x.
Question 4 NON-CALCULATOR [3 marks]
Each interior angle of a regular polygon is 140°. Show that the polygon has 9 sides.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
(9 − 2) × 180 = 7 × 180 = 1260°
▸ (9 − 2) × 180 M1
▸ 1260° A1
Question 2 [2 marks]
1260 ÷ 9 = 140°
▸ ((9 − 2) × 180)/9 M1
▸ 140° A1
Question 3 [3 marks]
Angle sum (6 − 2) × 180 = 720. 2x + 2x + 3x + 3x + 4x + 4x = 18x = 720, so x = 40.
▸ 720 M1
▸ 18x = 720 M1
▸ x = 40 A1
Question 4 [3 marks]
(n − 2) × 180 = 140n, so 180n − 360 = 140n, 40n = 360, n = 9. (Or: exterior angle 180 − 140 = 40, and 360 ÷ 40 = 9.)
▸ An equation (n − 2) × 180 = 140n, or the exterior angle 40 M1
▸ 40n = 360, or 360 ÷ 40 M1
▸ n = 9 with full working shown A1