NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1

NCERT Solutions of Class 9 Maths Chapter 6 Exercise 6.1

In this post, you can find a complete explanation of exercise 6.1 class 9 maths which belongs to Chapter 6 Lines and angles. Before you go through maths exercise 6.1 class 9, you should read and study the theorems of chapter 6.

NCERT Maths Class 9 Chapter 6 Exercise 6.1

Here you will find complete solutions to class 9 maths chapter 6 exercise 6.1 along with the video. You can watch videos related to ex 6.1 class 9 which will help you to understand the topic and questions of class 9 ex 6.1  lines and angles exercise 6.1. Questions of maths class 9 chapter 6 exercise 6.1are asked in the examination based on theorems of chapter 6 Lines and angles.

Class 9 Maths Chapter 6 Exercise 6.1

Ex 6.1 Q1

Ex 6.1 Q2

Ex 6.1 Q3

Ex 6.1 Q4

Ex 6.1 Q5

Ex 6.1 Q6

Video Ex 6.1

Let’s start solving questions of ex 6.1 class 9

Class 9 Maths Chapter 6 Exercise 6.1 Question 1

In the figure, lines AB and CD intersect at O. if ∠AOC+∠BOE=70° and ∠BOD=40°, find ∠BOE and reflex ∠COE.

Solution Question 1 ex 6.1 class 9 

 Here, ∠AOC= ∠BOD (vertically opposite angles)

Therefore, ∠AOC=40°   …………..(i)

Since  ∠BOD=40°                    (given)   

Now, ∠AOC+∠BOE=70°        (given)

So, , 40°+∠BOE=70°            (from (i))

Therefore, , ∠BOE=70°-40°=30°…………..(ii)

Now, ∠AOC+∠COB=180°    (leaner pair)

So, ∠AOC+∠COE+∠BOE=180°

Or    40°+∠COE+30°=180°    [from (i) and (ii)]

So, ∠COE=180°-40°-30°=110°

Therefore, Reflex ∠COE=360°-110°=250°

Class 9 Maths Chapter 6 Exercise 6.1 Question 2

In the figure, lines XY and MN intersect at O. if ∠POY=90° and a:b=2:3, find c.

Solution Question 2 ex 6.1 class 9 

 Here , a:b=2:3 and a+b= ∠POX=∠POY=90°

Let the angles be 2x and 3x

a=2x,b=3x

∠POX=a+b 

90°=2x+3x 

5x=90° 

x=`frac{90°}{5}`=18° 

a=2x=2×18°=36°  

b=3x=3×18°=54° 

Also, MN is a line 

Since ray OX stands on MN, therefore

∠MOX+∠XON=180°  (leaner pair)

b+c=180° 

⟹c+54°=180° 

⟹180°-54°=126° 

Hence c= 126°

Class 9 Maths Chapter 6 Exercise 6.1 Question 3

In the figure, if ∠PQR=∠PRQ, then prove that ∠PQS=∠PRT.

Solution Question 3 ex 6.1 class 9  

SRT is a line

Since QP stands on the line SRT

Therefore, ∠PQS+∠PQR=180° (linear pair)……….(i)

Since RP stands on the line SRT, 

Therefore, ∠PRQ+ ∠PRT=180° (linear pair)……(ii)

From (i) and (ii) , we have:

∠PQS+∠PQR=∠PRQ+∠PRT  ………..(iii)

Also, ∠PQR=∠PRQ  (given)………..(iv)

Subtracting (iv) from (iii), we have

∠PQS=∠PRT 

Hence proved

Class 9 Maths Chapter 6 Exercise 6.1 Question 4

In the figure, if x+y=w+z, then prove that AOB is a line.

Solution Question 4 ex 6.1 class 9 

Since the sum of all the angles around a point is equal to 360°

Therefore

(∠BOC+∠COA)+(∠BOD+∠AOD)=360°  

⟹            (x+y)+(w+z)=360° 

But           x+y=w+z            (given)

∴             x+y=w+z=`frac{360°}{2}`=180° 

Thus, ∠BOC and ∠COA as well as ∠BOD and ∠AOD form linear pairs. Consequently, OA and OB are two rays. Therefore AOB is a straight line.

Class 9 Maths Chapter 6 Exercise 6.1 Question 5

In the figure, PQR is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS=1/2 (∠QOS-∠POS).

Solution Question 5 ex 6.1 class 9 

 Since OR is perpendicular to the line PQ,

Therefore 

∠POR=∠ROQ 

Or        ∠POS+∠ROS=∠QOS-∠ROS 

⇒2∠ROS=∠QOS-∠POS 

⇒∠ROS=  `frac{1}{2}` (∠QOS-∠POS)   

Hence proved

Class 9 Maths Chapter 6 Exercise 6.1 Question 6

It is given that ∠XYZ=64° and XY is produced to point P. draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYP and reflex ∠QYP.

Solution Question 6 ex 6.1 class 9 

 

Since XY is produced to point P, therefore Xp is a straight line.

Now ray YZ stands XP

∴ ∠XYZ+ ∠ZYP=180°   (linear pair)

⟹  64°+∠ZYP=180° (∵∠XYZ=64°)

⟹     ∠ZYP=180°- 64°=116°  

Since ray YQ bisects ∠ZYP,

Therefore,

∠QYP=∠ZYQ=(116°)/2=58° 

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒      ∠XYQ=64°+58°=122°

And   reflex ∠QYP=180°+∠XYQ

∠QYP=180°+122°=302° 

Now you have understood the all questions of chapter 6 maths class 9 exercise 6.1, To better understand  6.1 maths class 9, watch the video given below.

Related Topics for you

1. Ex.6.2 Class 9 maths

2. All theorems chapter 6

3. Watch the Video of Exercise 6.1