Lines and Angles- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


    
                     
    
       
     
   
    
             
    
           
              
    
Q u e s t i o n : 1 5
In the given figure, OA and OB are opposite rays:
i
If x = 25°, what is the value of y?
Page 2


    
                     
    
       
     
   
    
             
    
           
              
    
Q u e s t i o n : 1 5
In the given figure, OA and OB are opposite rays:
i
If x = 25°, what is the value of y?
ii
If y = 35°, what is the value of x?
S o l u t i o n :
In figure:
Since OA and OB are opposite rays. Therefore, AB is a line. Since, OC stands on line AB.
Thus, and  form a linear pair, therefore, their sum must be equal to .
Or, we can say that
From the given figure:
 and 
On substituting these two values, we get
                             ...i
i
On putting in i
, we get:
Hence, the value of y is .
ii
On putting in in equation A
, we get:
Hence, the value of x is .
Q u e s t i o n : 1 6
In the given figure, write all pairs of adjacent angles and all the linear pairs.
Page 3


    
                     
    
       
     
   
    
             
    
           
              
    
Q u e s t i o n : 1 5
In the given figure, OA and OB are opposite rays:
i
If x = 25°, what is the value of y?
ii
If y = 35°, what is the value of x?
S o l u t i o n :
In figure:
Since OA and OB are opposite rays. Therefore, AB is a line. Since, OC stands on line AB.
Thus, and  form a linear pair, therefore, their sum must be equal to .
Or, we can say that
From the given figure:
 and 
On substituting these two values, we get
                             ...i
i
On putting in i
, we get:
Hence, the value of y is .
ii
On putting in in equation A
, we get:
Hence, the value of x is .
Q u e s t i o n : 1 6
In the given figure, write all pairs of adjacent angles and all the linear pairs.
S o l u t i o n :
The figure is given as follows:
The following are the pair of adjacent angles:
 and 
and 
The following are the linear pair:
 and 
and 
Q u e s t i o n : 1 7
In the given figure, find x. Further find ?BOC, ?COD and ?AOD
S o l u t i o n :
In the given figure:
AB is a straight line. Thus, ,  and  form a linear pair.
Therefore their sum must be equal to .
We can say that
 i
It is given that ,  and .
On substituting these values in i
, we get:
Page 4


    
                     
    
       
     
   
    
             
    
           
              
    
Q u e s t i o n : 1 5
In the given figure, OA and OB are opposite rays:
i
If x = 25°, what is the value of y?
ii
If y = 35°, what is the value of x?
S o l u t i o n :
In figure:
Since OA and OB are opposite rays. Therefore, AB is a line. Since, OC stands on line AB.
Thus, and  form a linear pair, therefore, their sum must be equal to .
Or, we can say that
From the given figure:
 and 
On substituting these two values, we get
                             ...i
i
On putting in i
, we get:
Hence, the value of y is .
ii
On putting in in equation A
, we get:
Hence, the value of x is .
Q u e s t i o n : 1 6
In the given figure, write all pairs of adjacent angles and all the linear pairs.
S o l u t i o n :
The figure is given as follows:
The following are the pair of adjacent angles:
 and 
and 
The following are the linear pair:
 and 
and 
Q u e s t i o n : 1 7
In the given figure, find x. Further find ?BOC, ?COD and ?AOD
S o l u t i o n :
In the given figure:
AB is a straight line. Thus, ,  and  form a linear pair.
Therefore their sum must be equal to .
We can say that
 i
It is given that ,  and .
On substituting these values in i
, we get:
It is given that:
Therefore,
Also,
Therefore,
Therefore,
Q u e s t i o n : 1 8
In the given figure, rays OA, OB, OC, OD and OE have the common end point O. Show that ?AOB + ?BOC + ?COD + ?DOE
+ ?EOA = 360°.
S o l u t i o n :
Let us draw a straight line.
, and form a linear pair. Thus, their sum should be equal to .
Or, we can say that:
 I
Similarly, , and form a linear pair. Thus, their sum should be equal to .
Page 5


    
                     
    
       
     
   
    
             
    
           
              
    
Q u e s t i o n : 1 5
In the given figure, OA and OB are opposite rays:
i
If x = 25°, what is the value of y?
ii
If y = 35°, what is the value of x?
S o l u t i o n :
In figure:
Since OA and OB are opposite rays. Therefore, AB is a line. Since, OC stands on line AB.
Thus, and  form a linear pair, therefore, their sum must be equal to .
Or, we can say that
From the given figure:
 and 
On substituting these two values, we get
                             ...i
i
On putting in i
, we get:
Hence, the value of y is .
ii
On putting in in equation A
, we get:
Hence, the value of x is .
Q u e s t i o n : 1 6
In the given figure, write all pairs of adjacent angles and all the linear pairs.
S o l u t i o n :
The figure is given as follows:
The following are the pair of adjacent angles:
 and 
and 
The following are the linear pair:
 and 
and 
Q u e s t i o n : 1 7
In the given figure, find x. Further find ?BOC, ?COD and ?AOD
S o l u t i o n :
In the given figure:
AB is a straight line. Thus, ,  and  form a linear pair.
Therefore their sum must be equal to .
We can say that
 i
It is given that ,  and .
On substituting these values in i
, we get:
It is given that:
Therefore,
Also,
Therefore,
Therefore,
Q u e s t i o n : 1 8
In the given figure, rays OA, OB, OC, OD and OE have the common end point O. Show that ?AOB + ?BOC + ?COD + ?DOE
+ ?EOA = 360°.
S o l u t i o n :
Let us draw a straight line.
, and form a linear pair. Thus, their sum should be equal to .
Or, we can say that:
 I
Similarly, , and form a linear pair. Thus, their sum should be equal to .
Or, we can say that:
 II
On adding I
and II
, we get:
Hence proved.
Q u e s t i o n : 1 9
In the given figure, ?AOC and ?BOC form a linear pair. If a - 2b = 30°, find a and b.
S o l u t i o n :
In the figure given below, it is given that and  forms a linear pair.
Thus, the sum of and  should be equal to .
Or, we can say that:
From the figure above, and 
Therefore,
It is given that:
On comparing i
and ii
, we get:
Putting  in i
, we get :