Class: VII
Subject: Math’s
Topic: Lines and angles
No. of Questions: 20
In fug 5.4, are the angles 1 and 2 of the letter N forming a pair of adjacent angles? Give reasons.
Sol.
No, ∠1 and ∠2 are not forming a pair of adjacent angles as they do not have a common
vertex.
Q2.
In fig. 5.6 AB EF, ED CD and ∠APE is 39o. Find ∠CQF.
Sol.
Since ED BE and AB is a transversal. So [Corresponding angles]
as
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ns
Q1
Or
∠QBP = 39o
Now AB EF and BC is a transversal.
Therefore, ∠FQB = ∠QBP
[Alternate interior angles]
Or ∠FQB = 39o
Also, ∠CQF + ∠ FQB = 180o
Or ∠CQF = 180o – 39o
Or ∠CQF = 141o
Q3
In fig. 5.7, CD intersects the line AB at F, ∠CFB = 50o and ∠EFA = ∠AFD. Find the measure of
∠EFC.
Sol.
Let ∠EFA =
Then ∠AFD = .
It is given that CD intersects line AB at F. Therefore, ∠CFB = ∠AFD
So,
= 50
But ∠EFA = ∠AFD which gives ∠EFA = 50o
ns
(Vertically opposite angles)
50o + 50o + ∠EFA = 180o
Or, ∠EFC = 180o – 100o
kI
Thus, ∠EFC = 80o.
IT
Or,
ia
Now, ∠CFB + ∠EFA +∠EFC = 180o [As AB is a straight line].
Find the complement of each of the following angles:
Sol.
The sum of the measures of complementary angles is 90o
as
Q4.
(i)
(ii)
(iii)
20o
Complement = 90o – 20o
= 70o
63o
Complement = 90 – 63o
= 27o
57o
Complement = 90o – 57o
= 33o
Find the supplement of each of the following angles:
Sol.
The sum of the measures of supplementary angles is 180o
(iii)
ia
(ii)
105o
Supplement = 180o – 105o
= 75o
87o Supplement = 180o – 87o
= 93o
154o
Supplement = 180o – 87o
= 26o
IT
(i)
ns
Q5.
Find the angle which is equal to its supplement
Sol.
Let the angle be x.
kI
Q6.
Supplement of this angle is also x.
as
The sum of the measures of a supplementary angles pair is 180o
∴ × + × = 180o
Q7.
Can two angles be supplementary if both of them are:
(i)
(ii)
(iii)
Acute?
Obtuse?
Right?
(i)
No. Acute angle is always lesser than 90o. If can be observed that two angles, even of
89o, cannot add up to 180o. Therefore, two acute angles cannot be in a
supplementary angle pair.
Sol.
(ii)
(iii)
No. Obtuse angle is always greater than 90o. It can be observed that two angles, even
of 91o, will always add up to more than 180o. Therefore, two obtuse angles cannot
be in a supplementary angle pair.
Yes, Right angles are of 90o + 90o = 180o
Therefore, two right angles for a supplementary angle pair together.
Q8.
An angle is greater than 45o. Is its complementary angle greater than 45o or equal to 45o?
Sol.
Let A and B are two angles making a complementary angle pair and A is greater than 415o.
A + B = 90o
ns
B = 90o – A
IT
Indicate which pairs of angles are:
(i)
(ii)
Vertically opposite anlges
Linear pairs.
(i)
∠1 and ∠4, and ∠5 and ∠2 + ∠3 are vertically opposite angles as these are formed
due to the intersection of two straight lines.
∠1 and ∠5, and ∠5 and ∠4 as these have a common vertex and also have noncommon arms opposite to each other.
as
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Q9.
ia
Therefore, B will be lesser than 45o.
Sol.
(ii)
Q10.
In the following figure, is ∠1 adjacent to ∠2? Give reason.
Sol.
∠1 and ∠2 are adjacent angle because their vertex is not common.
Q11.
Fill in the blank:
If two angles are complementary, then the sum of their measures is ----------.
If two angles are supplementary, then the sum of their measure is ------------.
Two angles forming a linear pair are ---------.
If two adjacent angles are supplementary, they form a --------.
If two lines intersect at a point, then the vertically opposite angles are always -------.
If two lines intersect at a point, and if one pair of vertically opposite angles are acute
angles, then the other of vertically opposite angles are ------.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
90o
180o
Supplementary
Linear pair
Equal
Obtuse angles
as
Q12.
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Sol.
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(i)
(ii)
(iii)
(iv)
(v)
(vi)
In the adjoining figure, name the following pairs of angles.
(i)
(ii)
(iii)
(iv)
Obtuse vertically opposite angles
Adjacent complementary angles
Equal Supplementary angles
Unequal supplementary angles
(v)
Adjacent angles that do not form a linear pair
(i)
(ii)
(iii)
(iv)
(v)
∠AOD, ∠BOC
∠EOA, ∠AOB
∠EOB, ∠EOD
∠EOA, ∠EOC
∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD
Sol.
State the property that is used in each of the following statements?
If a b, then ∠1 = ∠5
If ∠4 = ∠6, then a b
If ∠4 + ∠5 = 180o, then a b
IT
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(i)
(ii)
(iii)
ns
Q13.
(i)
(ii)
(iii)
Q14.
Corresponding angles property
Alternate interior angles property
Interior angles on the same side of transversal are supplementary.
as
Sol.
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1
In the adjoining figure, identify
(i)
(ii)
(iii)
(iv)
The pairs of corresponding angles
The pairs of alternate interior angles
The pairs of interior angles on the same side of the transversal
The vertically opposite angles
Sol.
∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
∠2 and ∠8, ∠3 and ∠5
∠2 and ∠5, ∠3 and ∠8
∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8
ns
(i)
(ii)
(iii)
(iv)
In the adjoining figure, p q. Find the unknown angles.
Sol.
∠d = 125o (Corresponding angles)
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Q15.
as
∠e = 180o – 125o = 50o (Linear pair)
∠f = ∠e = 55o (Vertically opposite angles)
∠c = ∠f = 55o (Corresponding angles)
∠a = ∠e = 55o (Corresponding angles)
∠b = ∠d = 125o (Vertically opposite angles)
Q16.
Find the value of x in each of the following figures if l m.
Sol.
∠x + ∠y = 180o (Linear pair)
= 70o
as
(ii)
kI
∠y =180o – 110o
IT
∠y = 110o (Corresponding angles)
ia
ns
(i)
∠x = 100o (Corresponding angles)
Q17.
In the given figure, the arms of two angles are parallel.
If ∠ABC = 70o, then find
(i)
(ii)
∠DGC
∠DEF
(i)
Consider that AB DG and a transversal line BC is intersecting them.
∠DGC = ∠ABC (Corresponding angles)
∠DGC = 70o
Consider that BC EF and a transversal line DE is intersecting them.
∠DEF = ∠DGC (Corresponding angles)
∠DEF = 70o
ia
In the given figures below, decide whether l is parallel to m.
as
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Q18.
IT
(ii)
ns
Sol.
Sol.
(i)
Consider two lines, land l and m, and a transversal line n which is intersecting them. Sum of
the interior angles on the same side of transversal = 126o + 44o = 170o As the sum of
interior angles on the same side of transversal is not 180o, therefore, l is not parallel to m.
IT
ia
ns
(ii)
x + 75o = 180o (Linear pair on line)
kI
x = 180o – 75o = 105o
(iii)
as
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be
equal. However, here their measures are 75o and 105o respectively. Hence, these lines are
not parallel to each other.
∠x + 123o =180o (Linear pair)
∠x = 180o – 123o = 57o
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be
equal. Here, their measures are 57o and 57o respectively. Hence, these are parallel to each
other.
(iv)
98 + ∠x = 180o (Linear pair)0
∠x =82o
ns
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be
equal. However, here their measures are 72o and 82o respectively. Hence, these lines are not
parallel to each other.
If a ray stands on a line, then the sum of two adjacent angles so formed is --------(0o/90o/180o/360o)
Sol.
180o
Q20.
Two lines in a plane can be_________(only intersecting/only parallel/both intersecting
parallel) lines.
Sol.
Both intersecting or parallel
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Q19.