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

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 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 :
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FAQs on Lines and Angles- 2 RD Sharma Solutions - Mathematics (Maths) Class 9

1. What are the different types of angles?
Ans. There are several types of angles, such as acute angles, right angles, obtuse angles, straight angles, and reflex angles. Acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, straight angles are exactly 180 degrees, and reflex angles are greater than 180 degrees.
2. How can we determine if two lines are parallel?
Ans. Two lines are parallel if they never intersect each other. One way to determine if two lines are parallel is by comparing their slopes. If the slopes of both lines are equal, then the lines are parallel. Another method is to use a transversal line that intersects the two lines. If the corresponding angles formed by the transversal are congruent, then the lines are parallel.
3. What is the sum of interior angles of a triangle?
Ans. The sum of the interior angles of a triangle is always equal to 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene. Each angle in a triangle can be represented by a letter, such as angle A, angle B, and angle C. The sum of these three angles will always be 180 degrees.
4. What is the difference between a line and a line segment?
Ans. A line is an infinite set of points that extends indefinitely in both directions. It has no endpoints. On the other hand, a line segment is a finite set of points that has two distinct endpoints. It is a portion of a line. A line segment can be measured and has a specific length, whereas a line has no measurable length.
5. How can we find the measure of an exterior angle of a polygon?
Ans. The measure of an exterior angle of a polygon can be found by subtracting the measure of the corresponding interior angle from 180 degrees. For example, if the measure of an interior angle of a polygon is 120 degrees, then the measure of its corresponding exterior angle would be 180 degrees - 120 degrees = 60 degrees. This property applies to all polygons, including triangles, quadrilaterals, and regular polygons.
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