Angle Sum Property of Polygons


 
 
Concept Explanation
 

Angle Sum Property of Polygons

Sum of interior angles of a polygon can be found by using the following rule

Angle Sum Property for a polygon with n number of sides:

If there is a polygon of n sides where n>=3, then we can cut it into n-2 triangles with a common vertex. For example if we have a polygon with five sides that is a pentagon then we can divide it into 5-2= 3 triangle from a common vertex as shown below

Now  we know that sum of angle of a triangle is 1800and a pentagon can be divided into 3 triangles

So the sum of interior angles of a triangle is 3 X 1800= 5400

So in general we can say that sum of interior angle of n sides polygon= (n-2) X 1800

Regular Polygon:

A regular polygon is a polygon which has sides of equal length and all interior angles are also equal. So if there is a regular polygon of n sides where n>= 3 then its each interior angle

 =frac{(n-2)times 180^0}{n}

Illustration: Find the sum of interior angles of a ten sides polygon.

Solution:The given polygon has 10 sides

The formula to find the sum of interior angles is = (n-2) X 1800 Where n is the number of sides of the polygon

It is given that n = 10

So sum of interior angles is

= (n-2) X 1800

= (10-2) X 1800

= 8 X 1800

= 14400

Hence the sum of interior angles of a 10 sided polygon is 14400.

Illustration: How many sides does a regular polygon has if its each angle is a measure of 1080?

Solution:Let us suppose the polygon has n sides

Then each interior angle is given by the formula

=frac{(n-2)times 180^0}{n}

According to the question each interior angle is = 1080

frac{(n-2)times 180^0}{n}=108^0

(n-2)times 180^0 =n times108^0

180n-360 =108 n

180n-108n=360

72n=360

n=frac{360 }{72}=5

Hence the regular polygon has 5 sides

Sample Questions
(More Questions for each concept available in Login)
Question : 1

What is the sum of interior angles of a pentagon ?

Right Option : C
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Explanation
Question : 2

What is the sum of interior angles of a triangle .

Right Option : D
View Explanation
Explanation
Question : 3

What is the sum of interior angles of a 4 sided figure .

Right Option : C
View Explanation
Explanation
 
 
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