NCERT Solutions for Class 7 Maths Exercise 6.3

NCERT Solutions for Class 7 Maths Exercise 6.3 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 7 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Maths Triangles and its Properties Download as PDF

NCERT Solutions for Class 7 Maths Triangles and its Properties

Class –VII Mathematics (Ex. 6.3)

Question 1.Find the value of unknown $x$ in the following diagrams:

Answer:

(i) In $\Delta {\text{ABC}},$

$\angle$BAC + $\angle$ACB + $\angle$ABC = $180^\circ$ [By angle sum property of a triangle]

$\Rightarrow$ $x + 50^\circ + 60^\circ = 180^\circ$

$\Rightarrow$ $x + 110^\circ = 180^\circ$ $\Rightarrow$ $x = 180^\circ – 110^\circ = 70^\circ$

(ii) In $\Delta$PQR,

$\angle$RPQ + $\angle$PQR + $\angle$RPQ = $180^\circ$ [By angle sum property of a triangle]

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

$\Rightarrow$ $x + 120^\circ = 180^\circ$ $\Rightarrow$ $x = 180^\circ – 120^\circ = 60^\circ$

(iii) In $\Delta$XYZ,

$\angle$ZXY + $\angle$XYZ + $\angle$YZX = $180^\circ$ [By angle sum property of a triangle]

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

$\Rightarrow$ $x + 140^\circ = 180^\circ$ $\Rightarrow$ $x = 180^\circ – 140^\circ = 40^\circ$

(iv) In the given isosceles triangle,

$x + x + 50^\circ = 180^\circ$ [By angle sum property of a triangle]

$\Rightarrow$ $2x + 50^\circ = 180^\circ$

$\Rightarrow$ $2x = 180^\circ – 50^\circ$ $\Rightarrow$ $2x = 130^\circ$

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

(v) In the given equilateral triangle,

$x + x + x = 180^\circ$ [By angle sum property of a triangle]

$\Rightarrow$ $3x = 180^\circ$

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

(vi) In the given right angled triangle,

$x + 2x + 90^\circ = 180^\circ$ [By angle sum property of a triangle]

$\Rightarrow$ $3x + 90^\circ = 180^\circ$

$\Rightarrow$ $3x = 180^\circ – 90^\circ$ $\Rightarrow$ $3x = 90^\circ$

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

---

NCERT Solutions for Class 7 Maths Exercise 6.3

Question 2.Find the values of the unknowns $x$ and $y$ in the following diagrams:

Answer:

(i) $50^\circ + x = 120^\circ$ [Exterior angle property of a $\Delta$ ]

$\Rightarrow$ $x = 120^\circ – 50^\circ = 70^\circ$

Now, $50^\circ + x + y = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $50^\circ + 70^\circ + y = 180^\circ$

$\Rightarrow$ $120^\circ + y = 180^\circ$ $\Rightarrow$ $y = 180^\circ – 120^\circ = 60^\circ$

(ii) $y = 80^\circ$ ……….(i) [Vertically opposite angle]

Now, $50^\circ + x + y = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $50^\circ + 80^\circ + y = 180^\circ$

[From eq. (i)]

$\Rightarrow$ $130^\circ + y = 180^\circ$ $\Rightarrow$ $y = 180^\circ – 130^\circ = 50^\circ$

(iii) $50^\circ + 60^\circ = x$ [Exterior angle property of a $\Delta$ ]

$\Rightarrow$ $x = 110^\circ$

Now $50^\circ + 60^\circ + y = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $110^\circ + y = 180^\circ$

$\Rightarrow$ $y = 180^\circ – 110^\circ$ $\Rightarrow$ $y = 70^\circ$

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

Now, $30^\circ + x + y = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $50^\circ + 60^\circ + y = 180^\circ$ [From eq. (i)]

$\Rightarrow$ $90^\circ + y = 180^\circ$ $\Rightarrow$ $y = 180^\circ – 90^\circ = 90^\circ$

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

Now, $y + x + x = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $90^\circ + 2x = 180^\circ$ [From eq. (i)]

$\Rightarrow$ $2x = 180^\circ – 90^\circ$ $\Rightarrow$ $2x = 90^\circ$

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

(vi) $x = y$ ……….(i) [Vertically opposite angle]

Now, $x + x + y = 180^\circ$ [Angle sum property of a $\Delta$ ]

$\Rightarrow$ $2x + x = 180^\circ$ [From eq. (i)]

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

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.