NCERT Solution - Lines & Angles Class 9 Notes | EduRev

Class 9 : NCERT Solution - Lines & Angles Class 9 Notes | EduRev

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Cbse-spot.blogspot.com  
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Class IX  Chapter 6 – Lines and 
Angles   Maths   
   
  
Exercise 6.1 Question 1:   
In the given figure, lines AB and CD intersect at O. If and   
   
find    
?   
BOE and reflex    
?   
COE.    
    
Answer:    
    
Question 2:    
Page 2


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 6 – Lines and 
Angles   Maths   
   
  
Exercise 6.1 Question 1:   
In the given figure, lines AB and CD intersect at O. If and   
   
find    
?   
BOE and reflex    
?   
COE.    
    
Answer:    
    
Question 2:    
Cbse-spot.blogspot.com  
2 
  
 
Let the common ratio between a and b be x.   
a = 2x, and b = 3x    
XY is a straight line, rays OM and OP stand on it.   
  XOM +  MOP +  POY = 180º  
b + a +  POY = 180º    
3x + 2x + 90º = 180º  
5x = 90º x = 18º a =  
2x = 2 × 18 = 36º b =  
3x= 3 ×18 = 54º    
MN is a straight line. Ray OX stands on it.   
 b + c = 180º (Linear Pair)  
54º + c = 180º c = 180º -  
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,    
find  c .     
    
Answer:    
Page 3


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 6 – Lines and 
Angles   Maths   
   
  
Exercise 6.1 Question 1:   
In the given figure, lines AB and CD intersect at O. If and   
   
find    
?   
BOE and reflex    
?   
COE.    
    
Answer:    
    
Question 2:    
Cbse-spot.blogspot.com  
2 
  
 
Let the common ratio between a and b be x.   
a = 2x, and b = 3x    
XY is a straight line, rays OM and OP stand on it.   
  XOM +  MOP +  POY = 180º  
b + a +  POY = 180º    
3x + 2x + 90º = 180º  
5x = 90º x = 18º a =  
2x = 2 × 18 = 36º b =  
3x= 3 ×18 = 54º    
MN is a straight line. Ray OX stands on it.   
 b + c = 180º (Linear Pair)  
54º + c = 180º c = 180º -  
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,    
find  c .     
    
Answer:    
Cbse-spot.blogspot.com  
3 
  
54º = 126º  
 c = 126º  
Question 3:   
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.   
   
Answer:   
In the given figure, ST is a straight line and ray QP stands on it.   
  PQS +  PQR = 180º (Linear Pair)   
PQR = 180º -  PQS (1)   
PRT + PRQ = 180º (Linear Pair)   
PRQ = 180º -  PRT (2)   
It is given that  PQR =  PRQ.   
Equating equations (1) and (2), we obtain   
 
180º - 
 
PQS = 180 - PRT PQS  
= PRT   
Page 4


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 6 – Lines and 
Angles   Maths   
   
  
Exercise 6.1 Question 1:   
In the given figure, lines AB and CD intersect at O. If and   
   
find    
?   
BOE and reflex    
?   
COE.    
    
Answer:    
    
Question 2:    
Cbse-spot.blogspot.com  
2 
  
 
Let the common ratio between a and b be x.   
a = 2x, and b = 3x    
XY is a straight line, rays OM and OP stand on it.   
  XOM +  MOP +  POY = 180º  
b + a +  POY = 180º    
3x + 2x + 90º = 180º  
5x = 90º x = 18º a =  
2x = 2 × 18 = 36º b =  
3x= 3 ×18 = 54º    
MN is a straight line. Ray OX stands on it.   
 b + c = 180º (Linear Pair)  
54º + c = 180º c = 180º -  
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,    
find  c .     
    
Answer:    
Cbse-spot.blogspot.com  
3 
  
54º = 126º  
 c = 126º  
Question 3:   
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.   
   
Answer:   
In the given figure, ST is a straight line and ray QP stands on it.   
  PQS +  PQR = 180º (Linear Pair)   
PQR = 180º -  PQS (1)   
PRT + PRQ = 180º (Linear Pair)   
PRQ = 180º -  PRT (2)   
It is given that  PQR =  PRQ.   
Equating equations (1) and (2), we obtain   
 
180º - 
 
PQS = 180 - PRT PQS  
= PRT   
Cbse-spot.blogspot.com  
4 
  
then prove that AOB is a line.   
= 360º (Complete angle) It is given 
that, x + y = z + w   x + y + x + y 
= 360º   
2(x + y) = 360º x  
+ y = 180º   
Since x and y form a linear pair, 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    
It can be observed that,  x + y + z + w   
Question 4:    
In the given figure, if    
    
Answer:    
Page 5


Cbse-spot.blogspot.com  
1 
  
  
Class IX  Chapter 6 – Lines and 
Angles   Maths   
   
  
Exercise 6.1 Question 1:   
In the given figure, lines AB and CD intersect at O. If and   
   
find    
?   
BOE and reflex    
?   
COE.    
    
Answer:    
    
Question 2:    
Cbse-spot.blogspot.com  
2 
  
 
Let the common ratio between a and b be x.   
a = 2x, and b = 3x    
XY is a straight line, rays OM and OP stand on it.   
  XOM +  MOP +  POY = 180º  
b + a +  POY = 180º    
3x + 2x + 90º = 180º  
5x = 90º x = 18º a =  
2x = 2 × 18 = 36º b =  
3x= 3 ×18 = 54º    
MN is a straight line. Ray OX stands on it.   
 b + c = 180º (Linear Pair)  
54º + c = 180º c = 180º -  
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,    
find  c .     
    
Answer:    
Cbse-spot.blogspot.com  
3 
  
54º = 126º  
 c = 126º  
Question 3:   
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.   
   
Answer:   
In the given figure, ST is a straight line and ray QP stands on it.   
  PQS +  PQR = 180º (Linear Pair)   
PQR = 180º -  PQS (1)   
PRT + PRQ = 180º (Linear Pair)   
PRQ = 180º -  PRT (2)   
It is given that  PQR =  PRQ.   
Equating equations (1) and (2), we obtain   
 
180º - 
 
PQS = 180 - PRT PQS  
= PRT   
Cbse-spot.blogspot.com  
4 
  
then prove that AOB is a line.   
= 360º (Complete angle) It is given 
that, x + y = z + w   x + y + x + y 
= 360º   
2(x + y) = 360º x  
+ y = 180º   
Since x and y form a linear pair, 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    
It can be observed that,  x + y + z + w   
Question 4:    
In the given figure, if    
    
Answer:    
Cbse-spot.blogspot.com  
5 
  
 
 POR = 90º   
 POS + SOR = 90º   
ROS = 90º - POS … (1)   
QOR = 90º (As OR  PQ)   
QOS - ROS = 90º    
ROS = QOS - 90º … (2)   
On adding equations (1) and (2), we obtain   
 ROS = QOS - POS 2   
ROS = QOS - POS) (   
Question 6:   
It is given that XYZ = and XY is produced to point P. Draw a figure from the 
given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.   
Answer:   
  
It is given that OR    PQ    
    
    
Answer:    
? 
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