EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Exterior Angles
Exterior angles of a polygon · Angles and trigonometry · Lesson 3 of 7 · 9 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 size of each exterior angle of a regular octagon.
Question 2 NON-CALCULATOR [2 marks]
Each interior angle of a regular polygon is 160°. Work out the number of sides of the polygon.
Question 3 NON-CALCULATOR [3 marks]
The diagram shows a regular hexagon and a square. They share a side. Work out the size of angle x.
Question 4 NON-CALCULATOR [2 marks]
Ali says, "I have drawn a regular polygon with exterior angles of 50°." Explain why Ali cannot be right.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
360 ÷ 8 = 45°
▸ 360 ÷ 8 M1
▸ 45° A1
Question 2 [2 marks]
Exterior angle 180 − 160 = 20°. 360 ÷ 20 = 18 sides.
▸ 180 − 160 = 20 M1
▸ 18 A1
Question 3 [3 marks]
Interior angle of the hexagon: 180 − 360 ÷ 6 = 120°. Interior angle of the square: 90°. Angles around a point: x = 360 − 120 − 90 = 150°.
▸ 120° for the hexagon's interior angle M1
▸ 360 − 120 − 90 M1
▸ 150° A1
Question 4 [2 marks]
360 ÷ 50 = 7.2. The number of sides must be a whole number, so no regular polygon has exterior angles of 50°.
▸ 360 ÷ 50 M1
▸ 7.2 and a statement that it is not a whole number C1