INTERIOR AND EXTERIOR ANGLES OF POLYGONS WORKSHEET

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

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

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

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

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

1. Answer :

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

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

2. Answer :

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°

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

3. Answer :

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°

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

4. Answer :

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

n ⋅ 20°  =  360°

n ⋅ 20  =  360

Divide both sides by 20.

n  =  18

So, the regular polygon has 18 sides. 

5. Answer :

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

x ⋅ 14.4°  =  360°

x ⋅ 14.4  =  360

Divide both sides by 14.4

x  =  25

So, the regular polygon has 25 sides. 

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