INTERIOR AND EXTERIOR ANGLES OF POLYGONS WORKSHEET

About "Interior and Exterior Angles of Polygons Worksheet"

Interior and Exterior Angles of Polygons Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on interior and exterior angles. 

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Interior and Exterior Angles of Polygons Worksheet -  Problems

Problem 1 :

What is the sum of the exterior angles of an octagon ?

Problem 2 :

What is the measure of one exterior angle of a regular decagon (ten-sided polygon) ?

Problem 3 :

What is the measure of each interior angle of a regular nonagon (nine-sided polygon) ?

Problem 4 :

One exterior angle of a regular polygon is 20°. How many sides does it have ?

Problem 5 :

One interior angle of a regular polygon is 165.6°. How many sides does it have ?

Interior and Exterior Angles of Polygons Worksheet -  Solution

Problem 1 :

What is the sum of the exterior angles of an octagon ?

Solution : 

In any polygon, the sum of all exterior angles is 360°.

So, the sum of the exterior angles of an octagon is also 360°.

Problem 2 :

What is the measure of one exterior angle of a regular decagon (ten-sided polygon) ?

Solution : 

In any polygon, the sum of all exterior angles is 360°.

The given decagon is a regular polygon.

So, all its exterior angles are of same measure. 

Because decagon is a ten-sided polygon, the measure of each exterior angle is

=  360° / 10

=  36°

Hence, the measure of each exterior exterior angle of a regular decagon is 36°.   

Problem 3 :

What is the measure of each interior angle of a regular nonagon (nine-sided polygon) ?

Solution : 

In any polygon, the sum of all exterior angles is 360°.

The given nonagon is a regular polygon.

So, all its exterior angles are of same measure. 

Because nonagon is a nine-sided polygon, the measure of each exterior angle is

=  360° / 9

=  40°

The measure of each exterior exterior angle of a regular nonagon is 40°. 

In any polygon, the sum of an interior angle and its corresponding exterior angle is 180°.

That is,

Interior angle + Exterior Angle  =  180°

Interior angle + 40°  =  180°

Interior angle  =  140°

Hence, the measure of each exterior exterior angle of a regular nonagon is 140°.   

Problem 4 :

One exterior angle of a regular polygon is 20°. How many sides does it have ?

Solution : 

Let the given regular polygon has "n" number of sides. 

The sum of all exterior angles of a polygon with "n" sides is 

=  No. of sides ⋅ Measure of each exterior angle

=  n ⋅ 20° ------(1)

In any polygon, the sum of all exterior angles is

=  360° ------(2)

From (1) and (2), we have

⋅ 20°  =  360°

⋅ 20  =  360

Divide both sides by 20.

n  =  18

Hence, the regular polygon has 18 sides. 

Problem 5 :

One interior angle of a regular polygon is 165.6°. How many sides does it have ?

Solution : 

Let the given regular polygon has "x" number of sides. 

In any polygon, the sum of an interior angle and its corresponding exterior angle is 180°.

That is,

Interior angle + Exterior Angle  =  180°

165.6° + Exterior Angle  =  180°

Exterior angle  =  14.4°

So, the measure of each exterior angle is 14.4°

The sum of all exterior angles of a polygon with "n" sides is 

=  No. of sides ⋅ Measure of each exterior angle

=  x ⋅ 14.4° ------(1)

In any polygon, the sum of all exterior angles is

=  360° ------(2)

From (1) and (2), we have

⋅ 14.4°  =  360°

⋅ 14.4  =  360

Divide both sides by 14.4

x  =  25

Hence, the regular polygon has 25 sides. 

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