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
In a regular hexagon measure of each of angle is _____________.. | |||
| Right Option : A | |||
| View Explanation | |||
What is the sum of interior angles of a triangle . | |||
| Right Option : D | |||
| View Explanation | |||
What is the sum of interior angles of a pentagon ? | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas 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
10thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thAbout 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
8thOne 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.
Aman Kumar Shrivastava
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thIt 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
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thA 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
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
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
Ayan Ghosh
8thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
8thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thMy 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
7thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thIt 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
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thMy 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.
