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

In this section, we are going to see the sum of exterior angles of a polygon.

**In any polygon (regular or irregular), the sum of exterior angle is **

**360**°

**Formula to find the number of sides of a**** ****regular**** polygon (****when the measure of each exterior angle is known)**** : **

**360 / Measure of each exterior angle**

**Formula to find the measure of each exterior angle of a ****regular**** polygon ****(****when the number of sides "n" given)**** : **

**360**° **/ n**

**In any polygon, the sum of an interior angle and its corresponding exterior angle is : **

**180°**

**Regular Polygon : **

**A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. **

**Irregular Polygon :**

**An irregular polygon can have sides of any length and angles of any measure. **

**Interior Angle :**

An interior angle of a polygon is an angle inside the polygon at one of its vertices.

**Exterior Angle :**

An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.

**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)° and 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"

Apart from the stuff given above, If you want to know more about "Sum of exterior angles of a polygon",please click here

Apart from the stuff given on "Sum of exterior angles of a polygon", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**