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  1. Maths
  2. Year 9
  3. Lines, Angles and Degrees
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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.

'Interior and Exterior Angles of Regular Polygons' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Illustrate Properties of Plane Figures

Difficulty level:  

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Worksheet Overview

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?

 

Answer

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?

  • ANSWERS
  • Question 1

A regular polygon has 8 sides.

 

Calculate its exterior angle.

 

(just write the number)

CORRECT ANSWER
45
EDDIE SAYS
360 ÷ 8
  • ANSWERS
  • Question 2

A regular polygon has 8 sides.

 

Calculate its interior angle.

 

(just write the number)

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

A regular polygon has 10 sides.

 

Calculate its exterior angle.

 

(just write the number)

CORRECT ANSWER
36
EDDIE SAYS
Exterior: 360 ÷ 10
  • ANSWERS
  • Question 4

A regular polygon has an exterior angle of 24º.

 

Calculate how many sides it has.

CORRECT ANSWER
15
EDDIE SAYS
Sides: 360 ÷ 24
  • ANSWERS
  • Question 5

A regular polygon has 12 sides.

 

Calculate its exterior angle.

 

(just write the number)

CORRECT ANSWER
30
EDDIE SAYS
Exterior: 360 ÷ 12
  • ANSWERS
  • Question 6

A regular polygon has 12 sides.

 

Calculate the sum of its interior angles.

 

(just write the number)

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

A regular polygon has 18 sides.

 

Calculate its interior angle.

 

(just write the number)

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

A regular polygon has 20 sides.

 

Calculate the sum of its interior angles.

 

(just write the number)

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

A regular polygon has an interior angle of 157½º.

 

How many sides does it have?

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

A regular polygon has an interior angle of 168¾º.

 

How many sides does it have?

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