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.

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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
Work out the sum of the interior angles of a pentagon.
Level 1 · 2 marksTry it
2
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
3
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
4
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
5
Work out the size of each interior angle of a regular polygon with 9 sides.
Level 2 · 2 marksTry it

15 more questions on interior & exterior angles of polygons

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