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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
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FAQs on Lines and Angles- 1 RD Sharma Solutions - Mathematics (Maths) Class 9

1. What are the types of angles?
Ans. There are several types of angles, including acute angles (less than 90 degrees), obtuse angles (between 90 and 180 degrees), right angles (exactly 90 degrees), and straight angles (exactly 180 degrees).
2. How do you identify parallel lines?
Ans. Parallel lines are lines that never intersect. To identify parallel lines, you can use the slope-intercept form of a line equation. If two lines have the same slope and different y-intercepts, they are parallel.
3. What is the sum of interior angles in a polygon?
Ans. The sum of the interior angles in a polygon can be calculated using the formula (n-2) * 180, where n represents the number of sides of the polygon.
4. How do you find the measure of an exterior angle of a triangle?
Ans. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. In other words, if the interior angles of a triangle are a, b, and c, then the measure of the exterior angle is equal to a + b.
5. What is the difference between vertical angles and adjacent angles?
Ans. Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They are always congruent, meaning they have the same measure. On the other hand, adjacent angles are two angles that share a common vertex and a common side but do not overlap. They can have different measures.
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