GCSE · Angles & polygons

Interior & exterior angles of polygonsExam-style questions

Why the exterior angles of any polygon add up to 360°, where (n − 2) × 180° comes from, how regular polygons follow instantly, and the reliable route from a given interior angle back to the number of sides.

Start practising Read the lesson

20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
The interior angles of a pentagon are $100°$ , $110°$ , $120°$ , $x°$ and $(x + 10)°$ .

Work out the value of $x$ . (3 marks)
Level 2 · 3 marksTry it
2
The exterior angle of a regular polygon is $24°$ .

(a) Work out the number of sides of the polygon. [2]

(b) Work out the size of each interior angle. [1]
Level 2 · 3 marksTry it
3
Five of the interior angles of a hexagon are $130°$ , $120°$ , $110°$ , $140°$ and $100°$ .

Work out the size of the sixth interior angle. [3]
Level 2 · 3 marksTry it
4
Work out the size of each interior angle of a regular polygon with 9 sides.
Level 2 · 2 marksTry it
5
A regular polygon has 10 sides.

(a) Work out the size of each exterior angle.

(b) Work out the size of each interior angle.
Level 2 · 2 marksTry it