Angles in regular polygons

The Maths Habit

A robot walks round a five sided track, turning at each corner.
When it is back at the start, facing the way it began, how far has it turned altogether?

One full turn: 360°, however many corners there are.

Regular polygon
All sides equal and all angles equal.
Interior angle
An angle inside the shape, at a corner.
Exterior angle
Carry a side straight on. The angle between that line and the next side.

Exterior angle = 360° ÷ number of sides
Interior angle = 180° − exterior angle

A regular polygon with 36 sides.
Find the exterior angle e and the interior angle i.

A regular polygon with 60 sides.
Find the exterior angle e and the interior angle i.

A regular polygon has 18 sides.

exterior angles of any polygon add to 360°
e = 360° ÷ 18 = 20°
i = 180° − 20° = 160°
Answer(a)20° (b)160°

A regular polygon has 24 sides.

e = 360° ÷ 24= 15°
i = 180° − 15° = 165°
Answer(a)15° (b)165°

A regular polygon has 18 sides.

exterior angles of any polygon add to 360°
e = 360° ÷ 18 = 20°
i = 180° − 20° = 160°
Answer(a)20° (b)160°

A regular polygon has 40 sides.

e = 360° ÷ 40 = 9°
i = 180° − 9° = 171°
Answer(a)9° (b)171°

A regular polygon has 18 sides.

exterior angles of any polygon add to 360°
e = 360° ÷ 18 = 20°
i = 180° − 20° = 160°
Answer(a)20° (b)160°

A regular polygon has 30 sides.

e = 360° ÷ 30 = 12°
i = 180° − 12° = 168°
Answer(a)12° (b)168°

A regular polygon has 18 sides.

exterior angles of any polygon add to 360°
e = 360° ÷ 18 = 20°
i = 180° − 20° = 160°
Answer(a)20° (b)160°

A regular polygon has 4 sides.

e = 360° ÷ 4 = 90°
i = 180° − 90° = 90°
Answer(a)90° (b)90°

A regular polygon has 18 sides.

exterior angles of any polygon add to 360°
e = 360° ÷ 18 = 20°
i = 180° − 20° = 160°
Answer(a)20° (b)160°

Each exterior angle of a regular polygon is 18°. Find (a) the number of sides and (b) the interior angle.

sides = 360° ÷ 18° = 20
i = 180° − 18° = 162°
Answer(a)20 (b)162°

Angles in regular polygons worksheet, page 1

Angles in regular polygons worksheet, page 2

Answer sheet

  1. The exterior angle of a regular polygon is 24°. How many sides does it have?

    15

  2. The interior angle of a regular polygon is 150°. How many sides does it have?

    12

  1. A regular polygon has 20 sides. Work out the size of each exterior angle.

    18°

  2. A regular polygon has 15 sides. Work out the size of each interior angle.

    156°

  3. Each exterior angle of a regular polygon is 40°. How many sides does it have?

    9
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