 # Exterior Angles of Regular Polygons

In this worksheet, students calculate the exterior angle of regular polygons. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive/Use the Sum of Angles for Deduction

Difficulty level:   ### QUESTION 1 of 10

Regular polygons have exterior angles which are all equal to each other.

Moreover they always add up to 360º.

To work out the size of each exterior angle of a regular polygon, we simply divide 360º by the number of angles.

The number of angles is equal to the number of sides.

Example

Work out the exterior angle of a regular hexagon.

The hexagon has 6 exterior angles as shown below. Each exterior angle is 360º ÷ 6 = 60º

Work out the exterior angle of a regular pentagon.

(just write the number) Work out the exterior angle of a square.

(just write the number)

Work out the exterior angle of a regular hexagon.

(just write the number) Work out the exterior angle of a regular octagon.

(just write the number) Work out the exterior angle of a regular nonagon.

(just write the number)

Work out the exterior angle of a regular decagon.

(just write the number)

Work out the exterior angle of a regular 12-sided polygon.

(just write the number)

Work out the exterior angle of a regular 15-sided polygon.

(just write the number)

Work out the exterior angle of a regular 18-sided polygon.

(just write the number)

Work out the exterior angle of a regular heptagon to the nearest whole degree.

(just write the number) • Question 1

Work out the exterior angle of a regular pentagon.

(just write the number) 72
• Question 2

Work out the exterior angle of a square.

(just write the number)

90
• Question 3

Work out the exterior angle of a regular hexagon.

(just write the number) 60
• Question 4

Work out the exterior angle of a regular octagon.

(just write the number) 45
• Question 5

Work out the exterior angle of a regular nonagon.

(just write the number)

40
• Question 6

Work out the exterior angle of a regular decagon.

(just write the number)

36
• Question 7

Work out the exterior angle of a regular 12-sided polygon.

(just write the number)

30
• Question 8

Work out the exterior angle of a regular 15-sided polygon.

(just write the number)

24
• Question 9

Work out the exterior angle of a regular 18-sided polygon.

(just write the number)

20
• Question 10

Work out the exterior angle of a regular heptagon to the nearest whole degree.

(just write the number) 51
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