1. /
2. CBSE
3. /
4. Class 07
5. /
6. Mathematics
7. /
8. NCERT Solutions for Class...

# NCERT Solutions for Class 7 Maths Exercise 6.3

### myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

NCERT solutions for Maths Triangles and its Properties

## NCERT Solutions for Class 7 Maths Triangles and its Properties

###### Question 1.Find the value of unknown {tex}x{/tex} in the following diagrams:

(i) In {tex}\Delta {\text{ABC}},{/tex}

{tex}\angle {/tex}BAC + {tex}\angle {/tex}ACB + {tex}\angle {/tex}ABC = {tex}180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}x + 50^\circ + 60^\circ = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x + 110^\circ = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}x = 180^\circ – 110^\circ = 70^\circ {/tex}

(ii) In {tex}\Delta {/tex}PQR,

{tex}\angle {/tex}RPQ + {tex}\angle {/tex}PQR + {tex}\angle {/tex}RPQ = {tex}180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}{90^ \circ } + {30^ \circ } + x = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x + 120^\circ = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}x = 180^\circ – 120^\circ = 60^\circ {/tex}

(iii) In {tex}\Delta {/tex}XYZ,

{tex}\angle {/tex}ZXY + {tex}\angle {/tex}XYZ + {tex}\angle {/tex}YZX = {tex}180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}{30^ \circ } + {110^ \circ } + x = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x + 140^\circ = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}x = 180^\circ – 140^\circ = 40^\circ {/tex}

(iv) In the given isosceles triangle,

{tex}x + x + 50^\circ = 180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}2x + 50^\circ = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}2x = 180^\circ – 50^\circ {/tex} {tex} \Rightarrow {/tex} {tex}2x = 130^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{130^\circ }}{2} = 65^\circ {/tex}

(v) In the given equilateral triangle,

{tex}x + x + x = 180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}3x = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{180^\circ }}{3} = 60^\circ {/tex}

(vi) In the given right angled triangle,

{tex}x + 2x + 90^\circ = 180^\circ {/tex} [By angle sum property of a triangle]

{tex} \Rightarrow {/tex} {tex}3x + 90^\circ = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}3x = 180^\circ – 90^\circ {/tex} {tex} \Rightarrow {/tex} {tex}3x = 90^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{90^\circ }}{3} = 30^\circ {/tex}

NCERT Solutions for Class 7 Maths Exercise 6.3

###### Question 2.Find the values of the unknowns {tex}x{/tex} and {tex}y{/tex} in the following diagrams:

(i) {tex}50^\circ + x = 120^\circ {/tex} [Exterior angle property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}x = 120^\circ – 50^\circ = 70^\circ {/tex}

Now, {tex}50^\circ + x + y = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}50^\circ + 70^\circ + y = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}120^\circ + y = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}y = 180^\circ – 120^\circ = 60^\circ {/tex}

(ii) {tex}y = 80^\circ {/tex} ……….(i) [Vertically opposite angle]

Now, {tex}50^\circ + x + y = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}50^\circ + 80^\circ + y = 180^\circ {/tex}

[From eq. (i)]

{tex} \Rightarrow {/tex} {tex}130^\circ + y = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}y = 180^\circ – 130^\circ = 50^\circ {/tex}

(iii) {tex}50^\circ + 60^\circ = x{/tex} [Exterior angle property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}x = 110^\circ {/tex}

Now {tex}50^\circ + 60^\circ + y = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}110^\circ + y = 180^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}y = 180^\circ – 110^\circ {/tex} {tex} \Rightarrow {/tex} {tex}y = 70^\circ {/tex}

(iv) {tex}x = {60^ \circ }{/tex} ……….(i) [Vertically opposite angle]

Now, {tex}30^\circ + x + y = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}50^\circ + 60^\circ + y = 180^\circ {/tex} [From eq. (i)]

{tex} \Rightarrow {/tex} {tex}90^\circ + y = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}y = 180^\circ – 90^\circ = 90^\circ {/tex}

(v) {tex}y = {90^ \circ }{/tex} ……….(i) [Vertically opposite angle]

Now, {tex}y + x + x = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}90^\circ + 2x = 180^\circ {/tex} [From eq. (i)]

{tex} \Rightarrow {/tex} {tex}2x = 180^\circ – 90^\circ {/tex} {tex} \Rightarrow {/tex} {tex}2x = 90^\circ {/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{{{90}^ \circ }}}{2} = {45^ \circ }{/tex}

(vi) {tex}x = y{/tex} ……….(i) [Vertically opposite angle]

Now, {tex}x + x + y = 180^\circ {/tex} [Angle sum property of a {tex}\Delta {/tex} ]

{tex} \Rightarrow {/tex} {tex}2x + x = 180^\circ {/tex} [From eq. (i)]

{tex} \Rightarrow {/tex} {tex}3x = 180^\circ {/tex} {tex} \Rightarrow {/tex} {tex}x = \frac{{180^\circ }}{3} = 60^\circ {/tex}

## NCERT Solutions for Class 7 Maths Exercise 6.3

NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

## CBSE app for Students

To download NCERT Solutions for Class 7 Maths, Social Science Computer Science, Home Science, Hindi English, Maths Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

myCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

### 5 thoughts on “NCERT Solutions for Class 7 Maths Exercise 6.3”

1. hey yeh math ka tension de jata hai hame papa se mar

2. Very nice

3. Superb explanation of sums

4. Nice one, I have to be the best price you, but I have, and the rest is the most of my life .

5. very useful