RD Sharma MCQs: Lines and Angles | Mathematics (Maths) Class 9 PDF Download

 Page 1


         
  
  
  
  
         
Q u e s t i o n : 8 6
One angle is equal to three times its supplement. The measure of the angle is
a
130°
b
135°
c
90°
d
120°
S o l u t i o n :
Let the supplement of the angle be
Therefore, according to the given statement, the required angle measures
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Thus, the supplement of angle measures
Hence, the correct choice is b
.
Q u e s t i o n : 8 7
Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD =
i
86°
Page 2


         
  
  
  
  
         
Q u e s t i o n : 8 6
One angle is equal to three times its supplement. The measure of the angle is
a
130°
b
135°
c
90°
d
120°
S o l u t i o n :
Let the supplement of the angle be
Therefore, according to the given statement, the required angle measures
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Thus, the supplement of angle measures
Hence, the correct choice is b
.
Q u e s t i o n : 8 7
Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD =
i
86°
ii
90°
iii
94°
iv
137°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting at a point .
Thus, ?AOD, ?AOC, ?COB and ?BOD
 form a complete angle, that is the sum of these four angle is .
That is,
?AOD + ?AOC + ?COB + ?BOD = 360°
                   ... i
It is given that
                               ...ii
Subtracting ii
from i
, we get:
Hence, the correct choice is a
.
Q u e s t i o n : 8 8
Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC =
a
63°
b
117°
c
17°
d
153°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting each other at a point .
Page 3


         
  
  
  
  
         
Q u e s t i o n : 8 6
One angle is equal to three times its supplement. The measure of the angle is
a
130°
b
135°
c
90°
d
120°
S o l u t i o n :
Let the supplement of the angle be
Therefore, according to the given statement, the required angle measures
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Thus, the supplement of angle measures
Hence, the correct choice is b
.
Q u e s t i o n : 8 7
Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD =
i
86°
ii
90°
iii
94°
iv
137°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting at a point .
Thus, ?AOD, ?AOC, ?COB and ?BOD
 form a complete angle, that is the sum of these four angle is .
That is,
?AOD + ?AOC + ?COB + ?BOD = 360°
                   ... i
It is given that
                               ...ii
Subtracting ii
from i
, we get:
Hence, the correct choice is a
.
Q u e s t i o n : 8 8
Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC =
a
63°
b
117°
c
17°
d
153°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting each other at a point .
Let the required angle  measures .
Also, and form a linear pair. Therefore, their sum must be equal to .
That is,
It is given that . Substituting, this value above, we get:
Hence, the correct choice is b
.
Q u e s t i o n : 8 9
Consider the following statements:
When two straight lines intersect:
i
adjacent angles are complementary
ii
adjacent angles are supplementary
iii
opposite angles are equal
iv
opposite angles are supplementary
Of these statements
 
a
i
and ii
are correct
b
ii
and iii
are correct
c
i
and iv
are correct
d
ii
and iv
  are correct
S o l u t i o n :
Page 4


         
  
  
  
  
         
Q u e s t i o n : 8 6
One angle is equal to three times its supplement. The measure of the angle is
a
130°
b
135°
c
90°
d
120°
S o l u t i o n :
Let the supplement of the angle be
Therefore, according to the given statement, the required angle measures
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Thus, the supplement of angle measures
Hence, the correct choice is b
.
Q u e s t i o n : 8 7
Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD =
i
86°
ii
90°
iii
94°
iv
137°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting at a point .
Thus, ?AOD, ?AOC, ?COB and ?BOD
 form a complete angle, that is the sum of these four angle is .
That is,
?AOD + ?AOC + ?COB + ?BOD = 360°
                   ... i
It is given that
                               ...ii
Subtracting ii
from i
, we get:
Hence, the correct choice is a
.
Q u e s t i o n : 8 8
Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC =
a
63°
b
117°
c
17°
d
153°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting each other at a point .
Let the required angle  measures .
Also, and form a linear pair. Therefore, their sum must be equal to .
That is,
It is given that . Substituting, this value above, we get:
Hence, the correct choice is b
.
Q u e s t i o n : 8 9
Consider the following statements:
When two straight lines intersect:
i
adjacent angles are complementary
ii
adjacent angles are supplementary
iii
opposite angles are equal
iv
opposite angles are supplementary
Of these statements
 
a
i
and ii
are correct
b
ii
and iii
are correct
c
i
and iv
are correct
d
ii
and iv
  are correct
S o l u t i o n :
Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point .
Now, let us consider each statement one by one:
i
When two lines intersect adjacent angles are complementary.
This statement is incorrect
Explanation:
As the adjacent angles form a linear pair and they are supplementary.
ii
When two lines intersect adjacent angles are supplementary.
This statement is correct.
Explanation:
As the adjacent angles form a linear pair and they are supplementary.
iii
When two lines intersect opposite angles are equal.
This statement is correct.
Explanation:
As the vertically opposite angles are equal.
iv
When two lines intersect opposite angles are supplementary.
This statement is incorrect.
Explanation:
As the vertically opposite angles are equal
Thus, out of all, ii
and iii
are correct.
Hence, the correct choice is b
.
Q u e s t i o n : 9 0
Given ?POR = 3x and ?QOR = 2x + 10°. If POQ is a straight line, then the value of x is
a
30°
b
34°
c
36°
Page 5


         
  
  
  
  
         
Q u e s t i o n : 8 6
One angle is equal to three times its supplement. The measure of the angle is
a
130°
b
135°
c
90°
d
120°
S o l u t i o n :
Let the supplement of the angle be
Therefore, according to the given statement, the required angle measures
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Thus, the supplement of angle measures
Hence, the correct choice is b
.
Q u e s t i o n : 8 7
Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD =
i
86°
ii
90°
iii
94°
iv
137°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting at a point .
Thus, ?AOD, ?AOC, ?COB and ?BOD
 form a complete angle, that is the sum of these four angle is .
That is,
?AOD + ?AOC + ?COB + ?BOD = 360°
                   ... i
It is given that
                               ...ii
Subtracting ii
from i
, we get:
Hence, the correct choice is a
.
Q u e s t i o n : 8 8
Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC =
a
63°
b
117°
c
17°
d
153°
S o l u t i o n :
Let us draw the following diagram showing two lines and  intersecting each other at a point .
Let the required angle  measures .
Also, and form a linear pair. Therefore, their sum must be equal to .
That is,
It is given that . Substituting, this value above, we get:
Hence, the correct choice is b
.
Q u e s t i o n : 8 9
Consider the following statements:
When two straight lines intersect:
i
adjacent angles are complementary
ii
adjacent angles are supplementary
iii
opposite angles are equal
iv
opposite angles are supplementary
Of these statements
 
a
i
and ii
are correct
b
ii
and iii
are correct
c
i
and iv
are correct
d
ii
and iv
  are correct
S o l u t i o n :
Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point .
Now, let us consider each statement one by one:
i
When two lines intersect adjacent angles are complementary.
This statement is incorrect
Explanation:
As the adjacent angles form a linear pair and they are supplementary.
ii
When two lines intersect adjacent angles are supplementary.
This statement is correct.
Explanation:
As the adjacent angles form a linear pair and they are supplementary.
iii
When two lines intersect opposite angles are equal.
This statement is correct.
Explanation:
As the vertically opposite angles are equal.
iv
When two lines intersect opposite angles are supplementary.
This statement is incorrect.
Explanation:
As the vertically opposite angles are equal
Thus, out of all, ii
and iii
are correct.
Hence, the correct choice is b
.
Q u e s t i o n : 9 0
Given ?POR = 3x and ?QOR = 2x + 10°. If POQ is a straight line, then the value of x is
a
30°
b
34°
c
36°
d
none of these
S o l u t i o n :
Let us draw the following figure, showing as a straight line.
Thus, and form a linear pair, therefore their sum must be supplementary. That is;
It is given that
and
On substituting these two values above, we get:
Hence, the correct choice is b
.
Q u e s t i o n : 9 1
In the given figure, AOB is a straight line. If ?AOC + ?BOD = 85°, then ?COD =
a
85°
b
90°
c
95°
d
100°
S o l u t i o n :
It is given that is a straight line.