Angle Sum Property of Polygons
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
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
According to the question each interior angle is = 1080
Hence the regular polygon has 5 sides
What is the sum of interior angles of a pentagon ? | |||
| Right Option : C | |||
| View Explanation | |||
In the figure given below, PTU is a straight line.
What is the value of x ? | |||
| Right Option : A | |||
| View Explanation | |||
Find the value of x when other four angles of a five sided figure are : 109, 105, 160, 40 | |||
| Right Option : D | |||
| View Explanation | |||
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