 # Interior and Exterior Angles of Regular Polygons

In this worksheet, students apply their knowledge of triangles to calculate the interior and exterior angles of regular polygons. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Illustrate Properties of Plane Figures

Difficulty level:   ### QUESTION 1 of 10

The following formulae for regular polygons should be known:

Exterior angle = 360º ÷ number of sides

Interior angle = 180º - exterior angle

Sum of interior angles = 180 x (number of sides - 2)

Example

A regular polygon has an interior angle of 165.6º.

How many sides does it have?

Exterior angle = 180 - interior angle = 180 - 165.6 = 14.4º

No. of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = 25

A regular polygon has 8 sides.

Calculate its exterior angle.

(just write the number)

A regular polygon has 8 sides.

Calculate its interior angle.

(just write the number)

A regular polygon has 10 sides.

Calculate its exterior angle.

(just write the number)

A regular polygon has an exterior angle of 24º.

Calculate how many sides it has.

A regular polygon has 12 sides.

Calculate its exterior angle.

(just write the number)

A regular polygon has 12 sides.

Calculate the sum of its interior angles.

(just write the number)

A regular polygon has 18 sides.

Calculate its interior angle.

(just write the number)

A regular polygon has 20 sides.

Calculate the sum of its interior angles.

(just write the number)

A regular polygon has an interior angle of 157½º.

How many sides does it have?

A regular polygon has an interior angle of 168¾º.

How many sides does it have?

• Question 1

A regular polygon has 8 sides.

Calculate its exterior angle.

(just write the number)

45
EDDIE SAYS
360 ÷ 8
• Question 2

A regular polygon has 8 sides.

Calculate its interior angle.

(just write the number)

135
EDDIE SAYS
Exterior: 360 ÷ 8 = 45 Interior: 180 - 45 = 135
• Question 3

A regular polygon has 10 sides.

Calculate its exterior angle.

(just write the number)

36
EDDIE SAYS
Exterior: 360 ÷ 10
• Question 4

A regular polygon has an exterior angle of 24º.

Calculate how many sides it has.

15
EDDIE SAYS
Sides: 360 ÷ 24
• Question 5

A regular polygon has 12 sides.

Calculate its exterior angle.

(just write the number)

30
EDDIE SAYS
Exterior: 360 ÷ 12
• Question 6

A regular polygon has 12 sides.

Calculate the sum of its interior angles.

(just write the number)

1800
EDDIE SAYS
Sum of interior angles: 180 × (12 - 2)
• Question 7

A regular polygon has 18 sides.

Calculate its interior angle.

(just write the number)

160
EDDIE SAYS
Exterior: 360 ÷ 18 = 20 Interior: 180 - 20 = 160
• Question 8

A regular polygon has 20 sides.

Calculate the sum of its interior angles.

(just write the number)

3240
EDDIE SAYS
Sum of Interior angles: 180 × (20 - 2)
• Question 9

A regular polygon has an interior angle of 157½º.

How many sides does it have?

16
EDDIE SAYS
Exterior: (180 - 157½) = 22.5 No of sides: 360 ÷ 22.5 = 16
• Question 10

A regular polygon has an interior angle of 168¾º.

How many sides does it have?

32
EDDIE SAYS
360 ÷ (180 - 168¾) Exterior: (180 - 168¾) = 11.25 No of sides: 360 ÷ 11.25 = 32
---- OR ----

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