Lines and Angles - Exercise 10.4 | Extra Documents & Tests for Class 9 PDF Download

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Q u e s t i o n : 4 7
In the given figure, AB CD and ?1 and ?2 are in the ratio 3:2 Determine all angles form 1 to 8.
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Q u e s t i o n : 4 7
In the given figure, AB CD and ?1 and ?2 are in the ratio 3:2 Determine all angles form 1 to 8.
S o l u t i o n :
The given figure is as follows:
It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2.
Let
In the figure angle 1 and 2 are supplementary. So,
3x + 2x = 180
? 5x = 180
? x = 36
?1 = 36 ×3 = 108° and ?2 = 36 ×2 = 72°
Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so
Since, angles 1 and 3 and 2 and 4 are vertically opposite angles, so
Now,
Angle 5 and 6 and angle 6 and 8 are vertically opposite angles, so
Hence, and .
Q u e s t i o n : 4 8
In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ?1, ?2 and ?3.
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Q u e s t i o n : 4 7
In the given figure, AB CD and ?1 and ?2 are in the ratio 3:2 Determine all angles form 1 to 8.
S o l u t i o n :
The given figure is as follows:
It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2.
Let
In the figure angle 1 and 2 are supplementary. So,
3x + 2x = 180
? 5x = 180
? x = 36
?1 = 36 ×3 = 108° and ?2 = 36 ×2 = 72°
Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so
Since, angles 1 and 3 and 2 and 4 are vertically opposite angles, so
Now,
Angle 5 and 6 and angle 6 and 8 are vertically opposite angles, so
Hence, and .
Q u e s t i o n : 4 8
In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ?1, ?2 and ?3.
S o l u t i o n :
According to the given figure,
m || n and are cut by transversal p.  
?2 = 120°         (alternate interior angles are equal)
Also, l || m. So, ?1 = ?3         (corresponding angles)
Also, ?3 and 120° form a linear pair.
?3 +120° = 180° ? ?3 = 180 -120 ? ?3 = 60°
And ?1 = ?3 = 60°, ?2 = 120°     
 
Q u e s t i o n : 4 9
In the given figure, if AB || CD and CD || EF, find ?ACE.
S o l u t i o n :
The figure is given as follows:
It is given that AB || CD and CD || EF
Thus, and  are alternate interior opposite angles.
Therefore,
Also, we have
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Q u e s t i o n : 4 7
In the given figure, AB CD and ?1 and ?2 are in the ratio 3:2 Determine all angles form 1 to 8.
S o l u t i o n :
The given figure is as follows:
It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2.
Let
In the figure angle 1 and 2 are supplementary. So,
3x + 2x = 180
? 5x = 180
? x = 36
?1 = 36 ×3 = 108° and ?2 = 36 ×2 = 72°
Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so
Since, angles 1 and 3 and 2 and 4 are vertically opposite angles, so
Now,
Angle 5 and 6 and angle 6 and 8 are vertically opposite angles, so
Hence, and .
Q u e s t i o n : 4 8
In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ?1, ?2 and ?3.
S o l u t i o n :
According to the given figure,
m || n and are cut by transversal p.  
?2 = 120°         (alternate interior angles are equal)
Also, l || m. So, ?1 = ?3         (corresponding angles)
Also, ?3 and 120° form a linear pair.
?3 +120° = 180° ? ?3 = 180 -120 ? ?3 = 60°
And ?1 = ?3 = 60°, ?2 = 120°     
 
Q u e s t i o n : 4 9
In the given figure, if AB || CD and CD || EF, find ?ACE.
S o l u t i o n :
The figure is given as follows:
It is given that AB || CD and CD || EF
Thus, and  are alternate interior opposite angles.
Therefore,
Also, we have
From the figure:
From equations i
and ii
:
Hence, the required value for is .
Q u e s t i o n : 5 0
In the given figure, state which lines are parallel and why.
S o l u t i o n :
The given figure is as follows:
Since
These are the pair of alternate interior opposite angles.
Theorem states: If a transversal intersects two lines in such a way that a pair of alternate interior angles is equal, then the
two lines are parallel.
Therefore,
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Q u e s t i o n : 4 7
In the given figure, AB CD and ?1 and ?2 are in the ratio 3:2 Determine all angles form 1 to 8.
S o l u t i o n :
The given figure is as follows:
It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2.
Let
In the figure angle 1 and 2 are supplementary. So,
3x + 2x = 180
? 5x = 180
? x = 36
?1 = 36 ×3 = 108° and ?2 = 36 ×2 = 72°
Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so
Since, angles 1 and 3 and 2 and 4 are vertically opposite angles, so
Now,
Angle 5 and 6 and angle 6 and 8 are vertically opposite angles, so
Hence, and .
Q u e s t i o n : 4 8
In the given figure, l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ?1, ?2 and ?3.
S o l u t i o n :
According to the given figure,
m || n and are cut by transversal p.  
?2 = 120°         (alternate interior angles are equal)
Also, l || m. So, ?1 = ?3         (corresponding angles)
Also, ?3 and 120° form a linear pair.
?3 +120° = 180° ? ?3 = 180 -120 ? ?3 = 60°
And ?1 = ?3 = 60°, ?2 = 120°     
 
Q u e s t i o n : 4 9
In the given figure, if AB || CD and CD || EF, find ?ACE.
S o l u t i o n :
The figure is given as follows:
It is given that AB || CD and CD || EF
Thus, and  are alternate interior opposite angles.
Therefore,
Also, we have
From the figure:
From equations i
and ii
:
Hence, the required value for is .
Q u e s t i o n : 5 0
In the given figure, state which lines are parallel and why.
S o l u t i o n :
The given figure is as follows:
Since
These are the pair of alternate interior opposite angles.
Theorem states: If a transversal intersects two lines in such a way that a pair of alternate interior angles is equal, then the
two lines are parallel.
Therefore,
Q u e s t i o n : 5 1
In the given figure, if l || m, n || p and ?1 = 85°, find ?2.
S o l u t i o n :
The figure is given as follows:
It is given that .
Thus, and  are corresponding angles.
Therefore,
It is given that . Therefore,
                ...i
Also, we have .
Thus, and  are consecutive interior angles.
Therefore,
From equation i
, we get:
Hence, the required value for is .
Q u e s t i o n : 5 2
If two straight lines are perpendicular to the same line, prove that they are parallel to each other.
S o l u t i o n :
The figure can be drawn as follows: