Lines and Angles- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 1
Write the complement of each of the following angles:
i
20°
ii
35°
iii
90°
iv
77°
v
30°
S o l u t i o n :
i
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of angle measures
ii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iv
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Page 2


Q u e s t i o n : 1
Write the complement of each of the following angles:
i
20°
ii
35°
iii
90°
iv
77°
v
30°
S o l u t i o n :
i
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of angle measures
ii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iv
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
v
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures .
Q u e s t i o n : 2
Write the supplement of each of the following angles:
i
54°
ii
132°
iii
138°
S o l u t i o n :
i
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
ii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
iii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Page 3


Q u e s t i o n : 1
Write the complement of each of the following angles:
i
20°
ii
35°
iii
90°
iv
77°
v
30°
S o l u t i o n :
i
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of angle measures
ii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iv
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
v
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures .
Q u e s t i o n : 2
Write the supplement of each of the following angles:
i
54°
ii
132°
iii
138°
S o l u t i o n :
i
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
ii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
iii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
Q u e s t i o n : 3
If an angle is 28° less than its complement, find its measure.
S o l u t i o n :
Let one angle be x°.
Then the required angle becomes
It is given that x° and are complementary
Therefore their sum must be equal to
On dividing both sides of the equation by 2,we get:
Also
Hence the measure of the required angle is .
Q u e s t i o n : 4
If an angle is 30° more than one half of its complement, find the measure of the angle.
S o l u t i o n :
Let the measure of the required angle be x°.
Thus its complement becomes 
According to the statement, the required angle is 30 more than half of its complementary angle that is; the required angle x
becomes,
.
Thus
Taking 2 on left hand side of the equation, we get
Hence, the required angle measures .
Page 4


Q u e s t i o n : 1
Write the complement of each of the following angles:
i
20°
ii
35°
iii
90°
iv
77°
v
30°
S o l u t i o n :
i
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of angle measures
ii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iv
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
v
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures .
Q u e s t i o n : 2
Write the supplement of each of the following angles:
i
54°
ii
132°
iii
138°
S o l u t i o n :
i
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
ii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
iii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
Q u e s t i o n : 3
If an angle is 28° less than its complement, find its measure.
S o l u t i o n :
Let one angle be x°.
Then the required angle becomes
It is given that x° and are complementary
Therefore their sum must be equal to
On dividing both sides of the equation by 2,we get:
Also
Hence the measure of the required angle is .
Q u e s t i o n : 4
If an angle is 30° more than one half of its complement, find the measure of the angle.
S o l u t i o n :
Let the measure of the required angle be x°.
Thus its complement becomes 
According to the statement, the required angle is 30 more than half of its complementary angle that is; the required angle x
becomes,
.
Thus
Taking 2 on left hand side of the equation, we get
Hence, the required angle measures .
Q u e s t i o n : 5
Two supplementary angles are in the ratio 4:5. Find the angles.
S o l u t i o n :
Let the two angles be 4x and 5x.
Since the angles are given as supplementary, therefore their sum must be equal to 
This can also be written as
Dividing both sides of equation by 9, we get
The two angles become
Also,
Hence, and  are the measure of two supplementary angles.
Q u e s t i o n : 6
Two supplementary angles differ by 48°. Find the angles.
S o l u t i o n :
Let one angle measures . Then, the second angle becomes .
Since the angles are supplementary, therefore their sum must be equal to .
Thus,
On dividing both sides of the equation by , we get
Also,
Hence, the required angles measure and .
Q u e s t i o n : 7
An angle is equal to 8 times its complement. Determine its measure.
S o l u t i o n :
Let the required angle be x°
Thus its complement becomes
Page 5


Q u e s t i o n : 1
Write the complement of each of the following angles:
i
20°
ii
35°
iii
90°
iv
77°
v
30°
S o l u t i o n :
i
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of angle measures
ii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iii
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
iv
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures
v
Let the complement of  angle measures x°
Since the angles are complementary, therefore their sum must be equal to
Or we can say that
Hence, the complement of  angle measures .
Q u e s t i o n : 2
Write the supplement of each of the following angles:
i
54°
ii
132°
iii
138°
S o l u t i o n :
i
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
ii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
iii
Let the supplement of  angle measures x°
Since the angles are supplementary, therefore their sum must be equal to
Or we can say that
Hence, the supplement of  angle measures .
Q u e s t i o n : 3
If an angle is 28° less than its complement, find its measure.
S o l u t i o n :
Let one angle be x°.
Then the required angle becomes
It is given that x° and are complementary
Therefore their sum must be equal to
On dividing both sides of the equation by 2,we get:
Also
Hence the measure of the required angle is .
Q u e s t i o n : 4
If an angle is 30° more than one half of its complement, find the measure of the angle.
S o l u t i o n :
Let the measure of the required angle be x°.
Thus its complement becomes 
According to the statement, the required angle is 30 more than half of its complementary angle that is; the required angle x
becomes,
.
Thus
Taking 2 on left hand side of the equation, we get
Hence, the required angle measures .
Q u e s t i o n : 5
Two supplementary angles are in the ratio 4:5. Find the angles.
S o l u t i o n :
Let the two angles be 4x and 5x.
Since the angles are given as supplementary, therefore their sum must be equal to 
This can also be written as
Dividing both sides of equation by 9, we get
The two angles become
Also,
Hence, and  are the measure of two supplementary angles.
Q u e s t i o n : 6
Two supplementary angles differ by 48°. Find the angles.
S o l u t i o n :
Let one angle measures . Then, the second angle becomes .
Since the angles are supplementary, therefore their sum must be equal to .
Thus,
On dividing both sides of the equation by , we get
Also,
Hence, the required angles measure and .
Q u e s t i o n : 7
An angle is equal to 8 times its complement. Determine its measure.
S o l u t i o n :
Let the required angle be x°
Thus its complement becomes
It is given that the angle x is 8 times its complementary angle, this means
Hence, the required angle measures .
Q u e s t i o n : 8
If the angles (2x - 10)° and (x - 5)° are complementary angles, find x.
S o l u t i o n :
It is given that and  are complementary angles.
Therefore, their sum must be equal to 90°.
Thus,
Hence the value of x is .
Q u e s t i o n : 9
If an angle differs from its complement by 10°, find the angle.
S o l u t i o n :
Let the angle measures x°
Therefore, the measure of its complement becomes
According to the question the above mentioned complementary angles differ by 10°.
Thus,
Hence the required angle measures .
Q u e s t i o n : 1 0
If the supplement of an angle is two-third of itself. Determine the angle and its supplement.
S o l u t i o n :
Let the angle measures x°.
Therefore, the measure of its supplement is