Interior and Exterior Angles of Regular Polygons
• Introduction

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?

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

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

• Question 1

A regular polygon has 8 sides.

Calculate its exterior angle.

(just write the number)

• Question 2

A regular polygon has 8 sides.

Calculate its interior angle.

(just write the number)

• Question 3

A regular polygon has 10 sides.

Calculate its exterior angle.

(just write the number)

• Question 4

A regular polygon has an exterior angle of 24º.

Calculate how many sides it has.

• Question 5

A regular polygon has 12 sides.

Calculate its exterior angle.

(just write the number)

• Question 6

A regular polygon has 12 sides.

Calculate the sum of its interior angles.

(just write the number)

• Question 7

A regular polygon has 18 sides.

Calculate its interior angle.

(just write the number)

• Question 8

A regular polygon has 20 sides.

Calculate the sum of its interior angles.

(just write the number)

• Question 9

A regular polygon has an interior angle of 157½º.

How many sides does it have?

• Question 10