**Sum of Exterior Angles of a Polygon Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on sum of exterior angles of a polygon.

Before look at the worksheet, if you would like to know the basic stuff about sum of exterior angles of a polygon,

**Problem 1 :**

Find the measure of each exterior angle of a regular decagon.

**Problem 2 :**

If the measure of each exterior angle of a regular pentagon is (2x + 4)°, find the value of x.

**Problem 3 :**

Find the measure of each exterior angle of the regular polygon given below.

**Problem 4 :**

Find the measure of exterior angle corresponding to the interior angle x° in the irregular polygon given below.

**Problem 5 :**

In a polygon, the measure of each interior angle is (5x+90)° and exterior angle is (3x-6)°. How many sides does the polygon have ?

**Problem 1 :**

Find the measure of each exterior angle of a regular decagon.

**Solution : **

Decagon is a 10-sided polygon.

In any polygon, the sum of exterior angles is

= 360°

**Formula to find the measure of each exterior angle of a ****regular**** ****n-sided ****polygon is :**

**360**° **/ n**

Then, we have

= 360° / 10

= 36°

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

**Problem 2 :**

If the measure of each exterior angle of a regular pentagon is (2x + 4)°, find the value of x.

**Solution : **

Pentagon is a 5-sided polygon.

In any polygon, the sum of exterior angles is

= 360°

**Formula to find the measure of each exterior angle of a ****regular**** ****n-sided ****polygon is :**

360° / n

Then, we have

= 360° / 5

= 72°

**The measure of each exterior angle is 72**°.

**Given : **The measure of each exterior angle of a regular pentagon is (2x + 4)°.

So, we have

(2x + 4)° = 72°

2x + 4 = 72

Subtract 4 from both sides.

2x = 68

Divide both sides by

x = 34

Hence, the value of "x" is 34.

**Problem 3 :**

Find the measure of each exterior angle of the regular polygon given below.

**Solution : **

Let us count the number of sides of the polygon given above.

So, the above regular polygon has 9 sides.

In any polygon, the sum of exterior angles is

= 360°

**Formula to find the measure of each exterior angle of a ****regular**** ****n-sided ****polygon is :**

**360**° **/ n**

Then, we have

= 360° / 9

= 40°

**Hence, the measure of each exterior angle of a regular polygon is **40°.

**Problem 4 :**

Find the measure of exterior angle corresponding to the interior angle x° in the irregular polygon given below.

**Solution : **

To find the measure of exterior angle corresponding to x° in the above polygon, first we have to find the value of x.

The above diagram is an irregular polygon of 6 sides (Hexagon) with one of the interior angles as right angle.

Formula to find the sum of interior angles of a n-sided polygon is

= (n - 2) ⋅ 180°

By using the formula, sum of the interior angles of the above polygon is

= (6 - 2) ⋅ 180°

= 4 ⋅ 180°

= 720° ------(1)

By using the angles, sum of the interior angles of the above polygon is

= 120° + 90° + 110° + 130° + 160 + x°

= 610° + x° ------(2)

From (1) and (2), we get

610° + x° = 720°

610 + x = 720

Subtract 610 from both sides.

x = 110

So, the measure of interior angle represented by x is 110°.

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

That is,

Interior angle + Exterior Angle = 180°

Then, we have

x° + Exterior Angle = 180°

110° + Exterior angle = 180°

Exterior angle = 70°

So, the measure of each exterior angle corresponding to x° in the above polygon is 20°.

**Problem 5 :**

In a polygon, the measure of each interior angle is (5x+90)° exterior angle is (3x-6)°. How many sides does the polygon have ?

**Solution : **

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

That is,

Interior angle + Exterior Angle = 180°

(5x + 90)° + (3x - 6)° = 180°

5x + 90 + 3x - 6 = 180

8x + 84 = 180

8x = 96

x = 12

Finding the measure of exterior angle :

Exterior angle = (3x-6)°

Exterior angle = (3 ⋅ 12 - 6)°

Exterior angle = (36 - 6)°

Exterior angle = 30°

Formula to find the number of sides of a regular polygon is

= 360 / Measure of each exterior angle

Then, we have

= 360 / 30

= 12

Hence, the given polygon has 12 sides.

After having gone through the stuff given above, we hope that the students would have understood, "Sum of exterior angles of a polygon worksheet"

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