The National Council of Educational Research and Training (NCERT) is an autonomous body of the Indian government that formulates the curricula for schools in India that are governed by the Central Board of Secondary Education (CBSE) and certain state boards. Therefore, students who will be taking the Class 10 tests administered by various boards should consult this NCERT Syllabus in order to prepare for those examinations, which in turn will assist those students get a passing score.

When working through the exercises in the NCERT textbook, if you run into any type of difficulty or uncertainty, you may use the swc NCERT Solutions for class 9 as a point of reference. While you are reading the theory form textbook, it is imperative that you always have notes prepared. You should make an effort to understand things from the very beginning so that you may create a solid foundation in the topic. Use the NCERT as your parent book to ensure that you have a strong foundation. After you have finished reading the theoretical section of the textbook, you should go to additional reference books.

NCERT Solutions for Class 9 Maths Exercise 6.1

Question 1. In Fig. 6.13, lines AB and CD intersect at O. If and, find and reflex.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image005.png

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image006.pngandNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image007.png.

We need to findNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image008.png.

From the given figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image009.pngform a linear pair.

We know that sum of the angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image011.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image012.pngor

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image013.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image014.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image015.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image016.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image017.png

Reflex NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image018.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image019.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image020.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image021.png(Vertically opposite angles), or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image022.png

But, we are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image023.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image024.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image025.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image026.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image027.pngandNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image028.png.

Question 2. In Fig. 6.14, lines XY and MN intersect at O. If and a:b = 2 : 3, find c.

file_2.tif

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image031.pngandNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image032.png.

We need find the value of c in the given figure.

Let a be equal to 2x and b be equal to 3x.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image033.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image034.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image036.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image037.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image038.png

ThereforeNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image039.png

NowNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image040.png[Linear pair]

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image041.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image042.png

Question 3. In the given figure,, then prove that .

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image045.jpg

Solution:
We need to prove thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image044.png.

We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image043.png.

From the given figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image046.pngform a linear pair.

We know that sum of the angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image047.pngand (i)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image048.png (ii)

From equations (i) and (ii), we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image049.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image050.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image051.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image052.png

Therefore, the desired result is proved.

Question 4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image053.jpg

Solution:
We need to prove that AOB is a line.

We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image054.png.

We know that the sum of all the angles around a fixed point isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image055.png.

Thus, we can conclude that

But, NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image054.png(Given).

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image058.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image059.png

From the given figure, we can conclude that y and x form a linear pair.

We know that if a ray stands on a straight line, then the sum of the angles of linear pair formed by the ray with respect to the line isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image060.png.

Therefore, we can conclude that AOB is a line.

Question 5. In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image062.jpg

Solution:
We need to prove thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image063.png.

We are given that OR is perpendicular to PQ, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image064.png

From the given figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image065.png form a linear pair.

We know that sum of the angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image066.pngNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image067.png, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image068.png.

From the figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image069.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.pngNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image070.png, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image071.png.(i)

From the given figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image072.pngform a linear pair.

We know that sum of the angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image073.png, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image074.png.(ii)

Substitute (ii) in (i), to get

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image075.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image076.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image077.png

Therefore, the desired result is proved.

Question 6. It is given thatand XY is produced to point P. Draw a figure from the given information. If ray YQ bisects, find 

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image078.png, XY is produced to P and YQ bisectsNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image079.png.

We can conclude the given below figure for the given situation:

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image081.jpg

We need to findNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image080.png.

From the given figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image082.pngform a linear pair.

We know that sum of the angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image083.png.

ButNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image078.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image084.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image085.png

Ray YQ bisectsNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image079.png, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image086.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image087.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image088.png

Reflex NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image089.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image090.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image091.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image092.pngand Reflex NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image093.png

NCERT Solutions for Class 9 Maths Exercise 6.2

Question 1. In figure, find the values of x and y and then show that AB || CD.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q1

Solution:
In the figure, we have CD and PQ intersect at F.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/q1
∴ y = 130° …(1)
[Vertically opposite angles]
Again, PQ is a straight line and EA stands on it.
∠AEP + ∠AEQ = 180° [Linear pair]
or 50° + x = 180°
⇒ x = 180° – 50° = 130° …(2)
From (1) and (2), x = y
As they are pair of alternate interior angles.
∴ AB || CD

Question 2. In figure, if AB || CD, CD || EF and y : z = 3 : 7, find x.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q2

Solution:
AB || CD, and CD || EF [Given]
∴ AB || EF
∴ x = z [Alternate interior angles] ….(1)
Again, AB || CD
⇒ x + y = 180° [Co-interior angles]
⇒ z + y = 180° … (2) [By (1)]
But y : z = 3 : 7
z = NCERT Solutions for Class 9 Maths Chapter-6 Lines and Anglesy = NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles(180°- z) [By (2)]
⇒ 10z = 7 x 180°
⇒ z = 7 x 180° /10 = 126°
From (1) and (3), we have
x = 126°.

Question 3. In figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q3

Solution:
AB || CD and GE is a transversal.
∴ ∠AGE = ∠GED [Alternate interior angles]
But ∠GED = 126° [Given]
∴∠AGE = 126°
Also, ∠GEF + ∠FED = ∠GED
or ∠GEF + 90° = 126° [∵ EF ⊥ CD (given)]
x = z [Alternate interior angles]… (1) Again, AB || CD
⇒ x + y = 180° [Co-interior angles]
∠GEF = 126° -90° = 36°
Now, AB || CD and GE is a transversal.
∴ ∠FGE + ∠GED = 180° [Co-interior angles]
or ∠FGE + 126° = 180°
or ∠FGE = 180° – 126° = 54°
Thus, ∠AGE = 126°, ∠GEF=36° and ∠FGE = 54°.

Question 4. In figure, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠QRS.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q4

Solution:
Draw a line EF parallel to ST through R.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/q4
Since PQ || ST [Given]
and EF || ST [Construction]
∴ PQ || EF and QR is a transversal
⇒ ∠PQR = ∠QRF [Alternate interior angles] But ∠PQR = 110° [Given]
∴∠QRF = ∠QRS + ∠SRF = 110° …(1)
Again ST || EF and RS is a transversal
∴ ∠RST + ∠SRF = 180° [Co-interior angles] or 130° + ∠SRF = 180°
⇒ ∠SRF = 180° – 130° = 50°
Now, from (1), we have ∠QRS + 50° = 110°
⇒ ∠QRS = 110° – 50° = 60°
Thus, ∠QRS = 60°.

Question 5. In figure, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q5

Solution:
We have AB || CD and PQ is a transversal.
∴ ∠APQ = ∠PQR
[Alternate interior angles]
⇒ 50° = x [ ∵ ∠APQ = 50° (given)]
Again, AB || CD and PR is a transversal.
∴ ∠APR = ∠PRD [Alternate interior angles]
⇒ ∠APR = 127° [ ∵ ∠PRD = 127° (given)]
⇒ ∠APQ + ∠QPR = 127°
⇒ 50° + y = 127° [ ∵ ∠APQ = 50° (given)]
⇒ y = 127°- 50° = 77°
Thus, x = 50° and y = 77°.

Question 6. In figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/Q6

Solution:
Draw ray BL ⊥PQ and CM ⊥ RS
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/q6
∵ PQ || RS ⇒ BL || CM
[∵ BL || PQ and CM || RS]
Now, BL || CM and BC is a transversal.
∴ ∠LBC = ∠MCB …(1) [Alternate interior angles]
Since, angle of incidence = Angle of reflection
∠ABL = ∠LBC and ∠MCB = ∠MCD
⇒ ∠ABL = ∠MCD …(2) [By (1)]
Adding (1) and (2), we get
∠LBC + ∠ABL = ∠MCB + ∠MCD
⇒ ∠ABC = ∠BCD
i. e., a pair of alternate interior angles are equal.
∴ AB || CD.

NCERT Solutions for Class 9 Maths Exercise 6.3

Question 1. In the given figure, sides QP and RQ of ∆PQR are produced to points S and T respectively. If SPR = 135º and PQT = 110º, find PRQ.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles Ex 6.3 Q1

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image003.png and NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image004.png.

We need to find the value ofNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image005.pngin the figure given below.

From the figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image006.pngform a linear pair.

We know that the sum of angles of a linear pair isNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image007.png.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image008.pngand NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image009.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image010.pngand NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image011.png

Or, NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image012.pngNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image013.png

From the figure, we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image014.pngNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image015.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image016.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image017.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image018.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image019.png.

Question 2. In the given figure, X = 62º, XYZ = 54º. If YO and ZO are the bisectors of XYZ and XZY respectively of ∆XYZ, find OZY and YOZ.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image020.jpg

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image021.pngand YO and ZO are bisectors ofNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image022.png, respectively.

We need to find NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image023.pngin the figure.

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image024.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image025.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image026.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image027.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image028.png

We are given that OY and OZ are the bisectors ofNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image022.png, respectively.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image029.pngand NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image030.png

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image031.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image032.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image033.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image034.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image035.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image036.pngandNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image037.png.

Question 3. In the given figure, if AB || DE, BAC = 35º and CDE = 53º, find DCE.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image038.png

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image039.png,NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image040.png.

We need to find the value of NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image041.pngin the figure given below.

From the figure, we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image042.png(Alternate interior)

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image043.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image044.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image046.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image047.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image048.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image049.png.

Question 4. In the given figure, if lines PQ and RS intersect at point T, such that PRT = 40º, RPT = 95º and TSQ = 75º, find SQT.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image050.jpg

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image051.png.

We need to find the value ofNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image052.pngin the figure.

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image053.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image054.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image055.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image056.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image057.png

From the figure, we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image058.png(Vertically opposite angles)

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image059.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image060.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image061.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image062.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image063.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image064.png.

Question 5. In the given figure, if, PQ || SR,, then find the values of x and y.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image067.jpg

Solution:
We are given thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image068.png.

We need to find the values of x and y in the figure.

We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”

From the figure, we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image069.png, or

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image070.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image071.png

From the figure, we can conclude that

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image072.png(Alternate interior angles)

From the figure, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image073.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image074.png(Angle sum property)

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image075.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image076.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image077.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image078.png

Therefore, we can conclude thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image079.png.

Question 6. In the given figure, the side QR of ∆PQR is produced to a point S. If the bisectors of meet at point T, then prove that.

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles

Solution:
We need to prove thatNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image081.pngin the figure given below.

We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image083.png,NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image084.pngis an exterior angle

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image085.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image086.png…(i)

From the figure, we can conclude that inNCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image083.png,NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image084.pngis an exterior angle

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image087.png

We are given that NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image088.pngare angle bisectors of NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image089.png

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image090.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image091.png

We need to substitute equation (i) in the above equation, to get

NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image092.png
NCERT Solutions for Class 9 Maths Chapter-6 Lines and Angles/image093.png

Therefore, we can conclude that the desired result is proved.

Conclusions for NCERT SOLUTIONS FOR CLASS 9 MATHS CHAPTER 6 LINES AND ANGLES

SWC academic staff has developed NCERT answers for this chapter of the ninth grade mathematics curriculum. We have solutions prepared for all of the exercises of this chapter. The answers, broken down into steps, to all of the questions included in the NCERT textbook’s chapter are provided here. Read this chapter on theory. Be certain that you have read the theory section of this chapter of the NCERT textbook and that you have learnt the formulas for the chapter that you are studying. 

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