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
(a) The size of each interior angle of a regular polygon is $156°$

Work out the number of sides of the polygon. (3 marks)
(b) A different regular polygon has $12$ sides.

Work out the size of each interior angle of this polygon. (1 mark)
Level 3 · 4 marksTry it
2
$P$ , $Q$ , $R$ , $S$ and $T$ are five consecutive vertices of a regular polygon with $n$ sides. $QRUVW$ is a regular pentagon.

$RSU$ is an equilateral triangle.

Work out the value of $n$ .

You must show all your working.

(4 marks)
Level 3 · 4 marksTry it
3
Each interior angle of a regular polygon is $162°$ .

Work out the number of sides of the polygon.
Level 3 · 3 marksTry it
4
The diagram shows a pentagon.Diagram NOT accurately drawn

Work out the size of the angle marked $x$ .
Level 3 · 3 marksTry it
5
Each exterior angle of a regular polygon is $24°$ .

Work out the number of sides of the polygon.
Level 3 · 2 marksTry it