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
Find the value of x when other four angles of a five sided figure are : 109, 105, 160, 40 | |||
| Right Option : D | |||
| View Explanation | |||
In a regular hexagon measure of each of angle is _____________.. | |||
| Right Option : A | |||
| View Explanation | |||
In the figure given below, PTU is a straight line.
What is the value of x ? | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [10]
It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
