Unit: 5: Lines and Angles
Exercise: 5.1 (14)
Question: 1
Find the complement of each of the following angles:
(i)

(ii)

(iii)

Solution
Complementary angle given angle
(i)
Complement of
(ii)
Complement of
(iii)
Complement of
Question: 2
Find the supplement of each of the following angles:
i.

ii.
iii.

Solution
Supplementary angle given angle
(i)
Supplement of
(ii)
Supplement of
(iii)
Supplement of
Question: 3
Identify which of the following pairs of angles are
complementary and which are supplementary.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution
If sum of two angles is ,
then they are called supplementary angles.
If sum of two angles is ,
then they are called complementary angles.
(i)
These are supplementary angles.
(ii)
These are complementary angles.
(iii)
These are supplementary angles.
(iv)
These are supplementary angles.
(v)
These are complementary angles.
(vi)
These are complementary angles.
Question: 4
Find the angle which is equal to its complement.
Solution
Let one of the two equal
complementary angles be .
Thus, is equal to its complement.
Question: 5
Find the angle which is equal to its supplement.
Solution
Let be two equal angles of its supplement.
Therefore, [Supplementary angles]
Thus, is equal to its supplement.
Question: 6
In the given figure, and are supplementary angles.

If is decreased, what changes should take place
in so that both the angles still remain
supplementary.
Solution
If is decreased then, will increase with the same measure, so that
both the angles still remain supplementary.
Question: 7
Can two angles be supplementary if both of them are:
(i)
acute?
(ii)
obtuse?
(iii)
right?
Solution
(i)
No, because sum of two acute angles is less than
(ii)
No, because sum of two obtuse angles is more
than
(iii)
Yes, because sum of two right angles is
Question: 8
An angle is greater than .
Is its complementary angle greater than or equal to or less than ?
Solution
Let the complementary angles be and .
It is given that
Adding both sides,
Thus, its complementary angle is less than
Question: 9
In the adjoining figure:

(i)
Is adjacent to ?
(ii)
Is adjacent to ?
(iii)
Do and form a linear pair?
(iv)
Are and supplementary?
(v)
Is vertically opposite to ?
(vi)
What is the vertically opposite angle of ?
Solution
(i)
Yes, in ,
OC is common arm.
(ii)
No, they have no non-common arms on opposite
side of common arm.
(iii)
Yes, they form linear pair.
(iv)
Yes, they are supplementary.
(v)
Yes, they are vertically opposite angles.
(vi)
Vertically opposite angles of is .
Question: 10
Indicate which pairs of angles are:
(i)
Vertically opposite angles.

(ii)
Linear pairs.
Solution
(i)
Vertically opposite angles, and ;
and + .
(ii)
Linear pairs and ;
and .
Question: 11
In the following figure, is adjacent to ?
Give reasons.

Solution
and are not adjacent angles because their vertex
is not common.
Question: 12
Find the values of the angles ,
,
and in
each of the following:
(i)

(ii)
Solution
(i)
[Vertically
opposite angles]
Now [Linear pair]
Also [Vertically
opposite angles]
Thus,
(ii)
[Angles on straight line]
Now [Linear pair]
……….(i)
Also [Linear pair]
[From
equation (i)]
Thus,
Question: 13
Fill in the blanks:
(i)
If two angles are complementary, then the sum of
their measures is ______________.
(ii)
If two angles are supplementary, then the sum of
their measures is ______________.
(iii)
Two angles forming a linear pair are
______________.
(iv)
If two adjacent angles are supplementary, they
form a ______________.
(v)
If two lines intersect at a point, then the
vertically opposite angles are always ______________.
(vi)
If two lines intersect at a point, and if one
pair of vertically opposite angles are acute angles, then the other pair of
vertically opposite angles are ______________.
Solution
(i)
If two angles are complementary, then the sum of
their measures is .
(ii)
If two angles are supplementary, then the sum of
their measures is .
(iii)
Two angles forming a linear pair are supplementary.
(iv)
If two adjacent angles are supplementary, they
form a linear pair.
(v)
If two lines intersect at a point, then the
vertically opposite angles are always equal.
(vi)
If two lines intersect at a point, and if one
pair of vertically opposite angles are acute angles, then the other pair of
vertically opposite angles are obtuse
angles.
Question: 14
In the adjoining figure, name the following pairs of angles.

(i)
Obtuse vertically opposite angles
(ii)
Adjacent complementary angles
(iii)
Equal supplementary angles
(iv)
Unequal supplementary angles
(v)
Adjacent angles that do not form a linear pair
Solution
(i)
(ii)
(iii)
(iv)
(v)
Exercise: 5.2 (6)
Question: 1
State the property that is used in each of the following
statements?
(i)
If then .
(ii)
If ,
then
(iii)
If ,
then

Solution
(i)
Given, then [Corresponding
angles]
If two parallel
lines are cut by a transversal, each pair of corresponding angles are equal in
measure.
(ii)
Given, ,
then [Alternate
interior angles]
When a
transversal cuts two lines such that pairs of alternate interior angles are
equal, the lines have to be parallel.
(iii)
Given, , then [Co-interior
Angles]
When a transversal
cuts two lines, such that pairs of interior angles on the same side of
transversal are supplementary, the lines have to be parallel.
Question: 2
In the adjoining figure, identify
(i)
the pairs of corresponding angles.
(ii)
the pairs of alternate interior angles.
(iii)
the pairs of interior angles on the same side of
the transversal.
(iv)
the vertically opposite angles.

Solution
(i)
The pairs of corresponding angles:
(ii)
The pairs of alternate interior angles are:
(iii)
The pair of interior angles on the same side of
the transversal:
(iv)
The vertically opposite angles are:
Question: 3
In the adjoining figure, Find the unknown angles.

Solution
Given, and cut by a transversal line.
[Linear pair]
……….(i)
Now [Vertically
opposite angles]
Also [Alternate
interior angles]
[Linear
pair]
[From
equation (i)]
Now [Vertically
opposite angles]
Thus,
Question: 4
Find the value of in
each of the following figures if
(i)

(ii)

(iii)

Solution
(i)
Given, and is transversal line.
Interior vertically opposite angle between
lines and
[Supplementary
angles]
(ii)
Given, and is transversal line.
[Interior
angles on same side of
transversal]
(iii)
Given, and .
[Corresponding
angles]
Question: 5
In the given figure, the arms of two angles are parallel. If
then find
(i)
(ii)

Solution
(i)
Given, and BC is a transversal line and
[Corresponding angles]
……….(i)
(ii)
Given, and DE is a transversal line and
[Corresponding
angles]
[From equation (i)]
Question: 6
In the given figures below, decide whether is
parallel to .
(i)

(ii)

(iii)

(iv)

Solution
(i)
l is not parallel to
m because sum of interior
angles on same side of transversal is not .
(ii)
because sum of angles on same side of transversal does not obey the property of parallel
lines.
(iii)
due to supplementary angles property of
parallel lines.
(iv)
is not parallel to because sum of angles does not obey the
property of parallel lines.