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
$PQRST$ is a pentagon.Angle $PTS$ is three times the size of angle $PQR$ .

Work out the size of angle $PTS$ .

You must show all your working.

(4 marks)
Level 4 · 4 marksTry it
2
The diagram shows a regular pentagon and a regular hexagon which have a common edge.Diagram NOT accurately drawn

Work out the size of the angle marked $a$ .
Level 4 · 4 marksTry it
3
Each interior angle of a regular polygon $P$ is 4 times the size of each exterior angle.

(a) Work out the number of sides of polygon $P$ .

Each interior angle of a regular polygon $Q$ is $6°$ bigger than each interior angle of polygon $P$ .

(b) Work out the number of sides of polygon $Q$ .
Level 4 · 5 marksTry it
4
Five of the interior angles of a hexagon are $130°$ , $145°$ , $105°$ , $118°$ and $132°$ .

Work out the size of the sixth interior angle.
Level 4 · 3 marksTry it
5
The sum of the interior angles of a polygon is $1440°$ .

(a) Work out the number of sides of the polygon.

The polygon is regular.

(b) Work out the size of each exterior angle.
Level 4 · 3 marksTry it