Like us!

Have a Look!

WhatsApp Message

Share Link

Angle Sum Property of a Triangle

Lines and Angles III - Concepts

Angle Sum Property of a Triangle

Exterior Angle Property

Class - 9th IMO Subjects

Concept Explanation

Angle Sum Property of a Triangle

Theorem: The sum of the three angles of a triangle is $large 180^{0}$

Given: A triangle ABC.

To Prove: $large angle A+angle B+angle C=180^{0}$ i.e. $large angle 1+angle 2+angle 3=180^{0}$

Construction: Through A, draw a line l parallel to BC.

Proof: Since $large lparallel BC$ . Therefore,

$large angle 2=angle 4$ [Alternate interior angles] .................(1)

and, $large angle 3=angle 5$ [Alternate interior angles] .................(2)

Adding equations (1),(2), we have

$large therefore ;;;;angle 2+angle 3=angle 4+angle 5$

$large Rightarrow ;;;angle 1+angle 2+angle 3=angle 1+angle 4+angle 5$ [Adding $large angle 1$ on both sides]

$large Rightarrow ;;;angle 1+angle 2+angle 3=angle 4+angle 1+angle 5$

$large Rightarrow ;angle 1+angle 2+angle 3=180^{0}$ [ $large because$ Sum of angles at a point on a line is $large 180^{circ}$

$large therefore$ $large angle 4+angle 1+angle 5=180^{circ}$ ]

$large Rightarrow;angle A+angle B+angle C=180^{0}$

Thus, the sum of the three angles of a triangle is $large 180^{0}$

Illustration: In a $bigtriangleup ABC,angle B=115^{0},angle C=45^{0}.$ Find $angle A$

Solution: Given: In $bigtriangleup ABC,angle B=115^{0},angle C=45^{0}.$ ...............(1)

By the angle sum property of a triangle, we have

$large angle A+angle B+angle C=180^{0}$

Using the values from equation (1), we have

$large angle A+115^{0}+45^{0}=180^{0}$

$large angle A+160^{0}=180^{0}$

$large angle A=180^{0}-160^{0}$

$large angle A=20^{0}$

Illustration: A, B, C are the three angles of a triangle. If $large A-B=15^{0},B-C=30^{0},$ Find $large angle A,angle B;and;angle C$ .

Solution: Given: $large A-B=15^{0}$ ..................(1)

$large A= B+15^{0}$ ..................(2)

and $large B-C=30^{0}$ ..................(3)

$large B= C+30^{0}$ ..................(4)

$large C= B-30^{0}$ ..................(5)

Using the angle sum property of a triangle

$large angle A+angle B+angle C=180^{0}$

Using equations (2),(5), we have

$large B+15^{0}+B+B-30^{0}=180^{0}$

$large 3B-15^{0}=180^{0}$

$large 3B=180^{0}+15^{0}$

$large 3B=195^{0}$

$large B=frac{195^{0}}{3}$

$large B=65^{0}$ .....................(6)

Using equation (6) in equations (2),(5), we have

$large A= B+15^{0}=65^{0}+15^{0}=80^{0}$

$large C= B-30^{0}=65^{0}-30^{0}=35^{0}$

Hence $large A=80^{0},;B=65^{0;},C=35^{0}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The sum of two angles of a triangle is equal to its third angle.Determine the measure of the third angle.
A. $60^0$	B. $90^0$	C. $75^0$	D. None of above
Right Option : B
View Explanation

Question : 2

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ___________________ .
A. an isosceles triangle	B. an obtuse triangle	C. an equilateral triangle	D. a right triangle
Right Option : D
View Explanation

Question : 3

If the angles of a triangle are in the ratio 2:1:3,then find the measure of smallest angle.
A. $40^0$	B. $60^0$	C. $30^0$	D. $75^0$
Right Option : C
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Polynomials II

Direct and Inverse Variation

Linear Equations in One Variable

Introduction to Trigonometry

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Constructions

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Class / Course

Students / Parents Reviews [10]

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

10th

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

8th

Being 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 m...

Prisha Gupta

8th

Abhyas 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

10th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

My 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

8th

One 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 develo...

Aman Kumar Shrivastava

10th

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

10th

It 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

10th

It 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

8th

View All

Attention !!!!!

Angle Sum Property of a Triangle

Angle Sum Property of a Triangle

Students / Parents Reviews [10]

Manish Kumar

Hiya Gupta

Prisha Gupta

Om Umang

Yatharthi Sharma

Ayan Ghosh

Aman Kumar Shrivastava

Barkha Arora

Cheshta

Eshan Arora