Chapter 5: Lines and Angles

Q1Written answer

The angles between North and West and South and East are

(a) complementary (b) supplementary

(c) both are acute (d) both are obtuse

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Solution:-

(b) supplementary

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 1

The angle between North and West is 90^o, the angle between South and East is 90^o, as shown in the figure above. So, 90^o + 90^o = 180^o.

Then, the angles between North and West and South and East are supplementary.

When the sum of the measures of two angles is 180°, then the angles are called supplementary angles.

Q2Written answer

Angles between South and West and South and East are

(a) vertically opposite angles (b) complementary angles

(c) making a linear pair (d) adjacent but not supplementary

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Solution:-

(c) making a linear pair

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

Q3Written answer

In Fig. 5.9, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ ABC = 46^o, then ∠ ABP is equal to

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 2

(a) 44^o (b) 67^o (c) 13^o (d) 62^o

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Solution:-

(b) 67^o

As we know that, the angle formed by the incident ray and angle formed by the reflected ray is equal.

From the given figure,

PQ is a straight line,

So, ∠ABP + ∠ABC + ∠CBQ = 180^o

Let us assume the ∠ABP = ∠CBQ = x

Then,

x + 46^o+ x = 180^o

2x + 46^o = 180^o

2x = 180^o – 46^o

2x = 134^o

x = 134^o/2

x = 67^o

Therefore, the ∠ABP = ∠CBQ = 67^o

Q4Written answer

If the complement of an angle is 79^o, then the angle will be of

(a) 1^o (b) 11^o (c) 79^o (d) 101^o

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Solution:-

(b) 11^o

When the sum of the measures of two angles is 90°, the angles are called complementary angles. Each of them is called complement of the other.

The given complement of an angle is 79^o

Let the measure of the angle be x^o.

Then,

x + 79^o = 90^o

x = 90^o – 79^o

x = 11^o

Hence, the measure of the angle is 11^o.

Q5Written answer

Angles which are both supplementary and vertically opposite are

(a) 95^o, 85^o (b) 90^o, 90^o (c) 100^o, 80^o (d) 45^o, 45^o

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Solution:-

(b) 90^o, 90^o

When the sum of the measures of two angles is 180°, then the angles are called supplementary angles.

Q6Written answer

The angle which makes a linear pair with an angle of 61^o is of

(a) 29^o (b) 61^o (c) 122^o (d) 119^o

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Solution:-

(d) 119^o

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

We know that, measure of sum of adjacent angles is equal to 180^o.

Let the measure of other angle be x^o.

Then,

x + 61^o = 180^o

x = 180^o – 61^o

x = 119^o

Q7Written answer

The angles x and 90^o – x are

(a) supplementary (b) complementary

(c) vertically opposite (d) making a linear pair

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Solution:-

(b) complementary

When the sum of the measures of two angles is 90^o, then the angles are called complementary angles.

x + 90^o – x = 90^o

90^o = 90^o

LHS = RHS

Q8Written answer

The angles x – 10^o and 190^o – x are

(a) interior angles on the same side of the transversal

(b) making a linear pair

(c) complementary

(d) supplementary

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Solution:-

(d) supplementary

When the sum of the measures of two angles is 180^o, then the angles are called supplementary angles.

x – 10^o + 190^o – x = 180^o

190^o – 10 = 180^o

180^o = 180^o

LHS = RHS

Q9Written answer

In Fig. 5.10, the value of x is

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 3

(a) 110^o (b) 46^o (c) 64^o (d) 150^o

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Solution:-

(d) 150^o

The sum of all angles about a point given in the figure is equal to 360^o.

Then, 100^o + 46^o + 64^o + x = 360^o

210^o + x = 360^o

x = 360^o – 210^o

x = 150^o

Q10Written answer

In Fig. 5.11, if AB || CD, ∠ APQ = 50^o and ∠PRD = 130^o, then ∠ QPR is

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 4

(a) 130^o (b) 50^o (c) 80^o (d) 30^o

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Solution:-

(c) 80^o

We know that, ∠APR = ∠PRD … [because interior alternate angles]

∠APQ + ∠QPR = 130^o

50^o + ∠QPR = 130^o

∠QPR = 130^o – 50^o

∠QPR = 80^o

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