Angles in regular polygons

The Maths Habit

1 Work out 360 ÷ 10

36

2 Work out 36 ÷ 4

9

3 Work out 180 − 40

140

A robot drives once round this path. It turns at every corner. When it is back at the start, facing the same way, how far has it turned?

One full turn: 360°.

Regular polygon
A flat shape with straight sides. All its sides are equal and all its angles are equal.
i
Interior angle
The angle inside the shape at a corner.
e
Exterior angle
Carry one side on. The angle between that line and the next side.
Full turn
Turning all the way round. It is 360°.

The exterior angles of a polygon add up to 360°.

1Exteriore=360÷sides=°
  1. Count the sides.
  2. Share 360° between the sides.A regular polygon has all its exterior angles equal.

A regular hexagon has 6 sides. Find e.

e
1Exteriore=360÷6=60°

A regular decagon has 10 sides. Find e.

e
1Exteriore=360÷10=36°

A regular hexagon has 6 sides. Find e.

e
1Exteriore=360÷6=60°

A square has 4 sides. Find e.

e
e1 Exterior e = 360 ÷ sides
1Exteriore=360÷4=90°

A regular hexagon has 6 sides. Find e.

e
1Exteriore=360÷6=60°

A regular nonagon has 9 sides. Find e.

e
e1 Exterior e = 360 ÷ sides
1Exteriore=360÷9=40°

A regular hexagon has 6 sides. Find e.

e
1Exteriore=360÷6=60°

An equilateral triangle has 3 sides. Find e.

e
e1 Exterior e = 360 ÷ sides
1Exteriore=360÷3=120°

1e

A regular polygon has 12 sides. Find e.

1Exteriore=360÷12=30°
2e

A regular polygon has 20 sides. Find e.

1Exteriore=360÷20=18°
360°

Each exterior angle is 60°. How many sides?

1Exteriore=360÷6=60°
e1 Exterior e = 360 ÷ sides

e and i make a straight line: 180°.

ei
1Exteriore=360÷sides=°
2Interiori=180−e=°
  1. Find e first.
  2. Take e away from 180°.What is left is i.

A regular nonagon has 9 sides. Find e and i.

ei
1Exteriore=360÷9=40°
2Interiori=180−40=140°

A square has 4 sides. Find e and i.

ei
1Exteriore=360÷4=90°
2Interiori=180−90=90°

A regular nonagon has 9 sides. Find e and i.

ei
1Exteriore=360÷9=40°
2Interiori=180−40=140°

A regular hexagon has 6 sides. Find e and i.

ei
ei1 Exterior e = 360 ÷ sides2 Interior i = 180 − e
1Exteriore=360÷6=60°
2Interiori=180−60=120°

A regular nonagon has 9 sides. Find e and i.

ei
1Exteriore=360÷9=40°
2Interiori=180−40=140°

A regular decagon has 10 sides. Find e and i.

ei
ei1 Exterior e = 360 ÷ sides2 Interior i = 180 − e
1Exteriore=360÷10=36°
2Interiori=180−36=144°

A regular nonagon has 9 sides. Find e and i.

ei
1Exteriore=360÷9=40°
2Interiori=180−40=140°

A regular polygon has 12 sides. Find e and i.

ei
ei1 Exterior e = 360 ÷ sides2 Interior i = 180 − e
1Exteriore=360÷12=30°
2Interiori=180−30=150°

1ei

An equilateral triangle has 3 sides. Find e and i.

1Exteriore=360÷3=120°
2Interiori=180−120=60°
2ei

A regular polygon has 20 sides. Find e and i.

1Exteriore=360÷20=18°
2Interiori=180−18=162°
345°i

Each exterior angle is 45°. Find i.

2Interiori=180−45=135°
ei1 Exterior e = 360 ÷ sides2 Interior i = 180 − e

Is it right? Thumbs up or thumbs down.

Aee = 60°Right
Bee = 180 ÷ 4 = 45°Wrong: 90°
Cii = 144°Right
Dii = 120°Wrong: 60°

Angles in regular polygons worksheet, page 1

Angles in regular polygons worksheet, page 2

Answer sheet

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

    12

  2. Can a regular polygon have an exterior angle of 50°? Explain how you know.

    No

  3. Work out the total of the interior angles of a regular hexagon.

    6 × 120° = 720°

  1. A regular nonagon has 9 sides. Find e and i. 1Exteriore=360÷9=40°2Interiori=180−40=140°

    e = 40°, i = 140°
    ei

  2. A regular hexagon has 6 sides. Find e and i. 1Exteriore=360÷6=60°2Interiori=180−60=120°

    e = 60°, i = 120°
    ei

  3. A regular decagon has 10 sides. Work out the size of each interior angle.

    144°
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