Angle Sum Property of Quadrilateral
Angle Sum Property of Quadrilateral
The word quad means four and the word lateral means sides. Thus, a plane figure bounded by four line segments AB, BC, CD and DA is called a quadrilateral and is written as quad. ABCD or, ABCD. The points A, B, C, D are called its vertices. The four line segments, AB, BC, CD and DA are the four sides, and the four angles
,
,
and
are the four angles of quad. ABCD, Two line segments AC and BD are called the diagonals of quad. ABCD.
Theorem : The sum of the four angles of a quadrilateral is 360.
|
GIVEN Quadrilateral ABCD To Prove <A + <B + <C + <D = 360 Construction Join BD Proof: In <1 + <2 + <3 = 180 .....(i) In <4 + <5 + <6 = 180 .......(ii) Adding (i) and (ii), we get <1 + <2 + <3 + <4 + <5 + <6 = 180 + 180 <1 + (<2 + <6 )+ <5+ (<3 + <4) = 180 + 180
|
 |
Illustration: In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2: 3 : 4. Find the measure of each angles of the quadrilateral.
Solution: We have, <A : <B : <C : <D = 1 : 2 : 3 : 4. So, let <A = x, <B = 2x, <C = 3x, < D = 4x.
<A + <B + <C + <D = 360
x + 2x + 3x + 4x = 360
10x = 360
x = 36
Thus, the angles are
The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. If measure of angles be | |||
| Right Option : B | |||
| View Explanation | |||
Find the value of x when other three angles are : 145, 66, 100 . | |||
| Right Option : A | |||
| View Explanation | |||
Find the value of x when other three angles are : 108, 70, 15 . | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
My 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
8thMy 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
8thIt 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
7thAbout 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
8thAbhyas 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
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
10thAbhyas 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
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.
Aman Kumar Shrivastava
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.
