Interior and Exterior Angles of Regular Polygons
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  • Introduction
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The following formulae for regular polygons should be known:

 

Exterior angle = 360º ÷ no. of sides


Interior angle = 180º - exterior angle


Sum of interior angles = 180 x (no. 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

  • Question 1
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A regular polygon has 8 sides.

 

Calculate its exterior angle.

 

(just write the number)

  • Question 2
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A regular polygon has 8 sides.

 

Calculate its interior angle.

 

(just write the number)

  • Question 3
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A regular polygon has 10 sides.

 

Calculate its exterior angle.

 

(just write the number)

  • Question 4
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A regular polygon has an exterior angle of 24º.

 

Calculate how many sides it has.

  • Question 5
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A regular polygon has 12 sides.

 

Calculate its exterior angle.

 

(just write the number)

  • Question 6
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A regular polygon has 12 sides.

 

Calculate the sum of its interior angles.

 

(just write the number)

  • Question 7
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A regular polygon has 18 sides.

 

Calculate its interior angle.

 

(just write the number)

  • Question 8
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A regular polygon has 20 sides.

 

Calculate the sum of its interior angles.

 

(just write the number)

  • Question 9
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A regular polygon has an interior angle of 157½º.

 

How many sides does it have?

  • Question 10
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A regular polygon has an interior angle of 168¾º.

 

How many sides does it have?

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