NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (2023 – 2024)

The NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles is the best study material for those students who are finding it difficult to solve problems. The solutions to all the questions in this chapter are provided by Study Circle in easy and simple language.

These NCERT Solutions can help the students to clear doubts instantly and understand the subject effectively. Students who want to score good marks in maths must practice NCERT Solutions for Class 7 Maths Chapter 5. All the questions of this chapter are based on the new syllabus.

The NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles has 2 exercises. Let us now have a look at some of the topics covered in this chapter and try to understand them.

 NCERT Solutions Class 7 Maths Chapter 5

Exercise 5.1

 

Question 1. Find the complement of each of the following angles:

(i)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be complementary if the sum of their measures is 90o.

The given angle is 20o

Let the measure of its complement be xo.

Then,

= x + 20o = 90o

= x = 90o – 20o

= x = 70o

Hence, the complement of the given angle measures 70o.

(ii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be complementary if the sum of their measures is 90o.

The given angle is 63o

Let the measure of its complement be xo.

Then,

= x + 63o = 90o

= x = 90o – 63o

= x = 27o

Hence, the complement of the given angle measures 27o.

(iii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be complementary if the sum of their measures is 90o.

The given angle is 57o

Let the measure of its complement be xo.

Then,

= x + 57o = 90o

= x = 90o – 57o

= x = 33o

Hence, the complement of the given angle measures 33o.

Question 2. Find the supplement of each of the following angles:

(i)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be supplementary if the sum of their measures is 180o.

The given angle is 105o

Let the measure of its supplement be xo.

Then,

= x + 105o = 180o

= x = 180o – 105o

= x = 75o

Hence, the supplement of the given angle measures 75o.

(ii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be supplementary if the sum of their measures is 180o.

The given angle is 87o

Let the measure of its supplement be xo.

Then,

= x + 87o = 180o

= x = 180o – 87o

= x = 93o

Hence, the supplement of the given angle measures 93o.

(iii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Two angles are said to be supplementary if the sum of their measures is 180o.

The given angle is 154o

Let the measure of its supplement be xo.

Then,

= x + 154o = 180o

= x = 180o – 154o

= x = 26o

Hence, the supplement of the given angle measures 93o.

Question 3. Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65o, 115o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 65o + 115o

= 180o

If the sum of two angles measures 180o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(ii) 63o, 27o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 63o + 27o

= 90o

If the sum of two angle measures is 90o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

(iii) 112o, 68o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 112o + 68o

= 180o

If the sum of two angle measures is 180o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(iv) 130o, 50o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 130o + 50o

= 180o

If the sum of two angle measures is 180o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(v) 45o, 45o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 45o + 45o

= 90o

If the sum of two angle measures is 90o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

(vi) 80o, 10o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 80o + 10o

= 90o

If the sum of two angle measures is 90o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

Question 4. Find the angle which is equal to its complement.

Solution:-

Let the measure of the required angle be xo.

We know that sum of measures of complementary angle pair is 90o.

Then,

= x + x = 90o

= 2x = 90o

= x = 90/2

= x = 45o

Hence, the angle which is equal to its complement is 45o.

Question 5. Find the angle which is equal to its supplement.

Solution:-

Let the measure of the required angle be xo.

We know that sum of measures of supplementary angle pair is 180o.

Then,

= x + x = 180o

= 2x = 180o

= x = 180/2

= x = 90o

Hence, the angle which is equal to its supplement is 90o.

Question 6. In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both angles still remain supplementary?

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

From the question, it is given that,

∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 must be increased by the same value. Hence, this angle pair remains supplementary.

Question 7. Can two angles be supplementary if both of them are:

(i). Acute?

Solution:-

No. If two angles are acute, which means less than 90o, the two angles cannot be supplementary because their sum will always be less than 90o.

(ii). Obtuse?

Solution:-

No. If two angles are obtuse, which means more than 90o, then two angles cannot be supplementary because their sum will always be more than 180o.

(iii). Right?

Solution:-

Yes. If two angles are right, which means both measure 90o, then two angles can form a supplementary pair.

∴90+ 90o = 180

Question 8. An angle is greater than 45o. Is its complementary angle greater than 45o or equal to 45o or less than 45o?

Solution:-

Let us assume the complementary angles be p and q,

We know that sum of measures of complementary angle pair is 90o.

Then,

= p + q = 90o

It is given in the question that p > 45o

Adding q on both sides,

= p + q > 45+ q

= 90o > 45+ q

= 90o – 45o > q

= q < 45o

Hence, its complementary angle is less than 45o.

Question 9. In the adjoining figure:

NCERT Solutions Class 7 Maths Chapter 5

(i) Is ∠1 adjacent to ∠2?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠1 and ∠2 have a common vertex, i.e. O and a common arm OC.

Their non-common arms, OA and OE, are on both sides of the common arm.

(ii) Is ∠AOC adjacent to ∠AOE?

Solution:-

By observing the figure, we came to conclude that,

No, since they have a common vertex O and common arm OA.

But they have no non-common arms on both sides of the common arm.

(iii) Do ∠COE and ∠EOD form a linear pair?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠COE and ∠EOD have a common vertex, i.e. O and a common arm OE.

Their non-common arms, OC and OD, are on both sides of the common arm.

(iv) Are ∠BOD and ∠DOA supplementary?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠BOD and ∠DOA have a common vertex, i.e. O and a common arm OE.

Their non-common arms, OA and OB, are opposite to each other.

(v) Is ∠1 vertically opposite to ∠4?

Solution:-

Yes, ∠1 and ∠2 are formed by the intersection of two straight lines AB and CD.

(vi) What is the vertically opposite angle of ∠5?

Solution:-

∠COB is the vertically opposite angle of ∠5 because these two angles are formed by the intersection of two straight lines AB and CD.

Question 10. Indicate which pairs of angles are:

NCERT Solutions Class 7 Maths Chapter 5

(i) Vertically opposite angles.

Solution:-

By observing the figure, we can say that,

∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles because these two angles are formed by the intersection of two straight lines.

(ii) Linear pairs.

Solution:-

By observing the figure, we can say that,

∠1 and ∠5, ∠5 and ∠4, as these have a common vertex and also have non-common arms opposite to each other.

Question 11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

∠1 and ∠2 are not adjacent angles because they are not lying on the same vertex.

12. Find the values of the angles x, y, and z in each of the following:

(i)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

∠x = 55o, because vertically opposite angles.

∠x + ∠y = 180o … [∵ linear pair]

= 55o + ∠y = 180o

= ∠y = 180o – 55o

= ∠y = 125o

Then, ∠y = ∠z … [∵ vertically opposite angles]

∴ ∠z = 125o

(ii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

∠z = 40o, because vertically opposite angles.

∠y + ∠z = 180o … [∵ linear pair]

= ∠y + 40o = 180o

= ∠y = 180o – 40o

= ∠y = 140o

Then, 40 + ∠x + 25 = 180o … [∵angles on straight line]

65 + ∠x = 180o

∠x = 180o – 65

∴ ∠x = 115o

Question 13. Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

Solution:-

If two angles are complementary, then the sum of their measures is 90o.

(ii) If two angles are supplementary, then the sum of their measures is ______.

Solution:-

If two angles are supplementary, then the sum of their measures is 180o.

(iii) Two angles forming a linear pair are _______________.

Solution:-

Two angles forming a linear pair are supplementary.

(iv) If two adjacent angles are supplementary, they form a ___________.

Solution:-

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

_____________.

Solution:-

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 __________.

Solution:-

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.

NCERT Solutions Class 7 Maths Chapter 5

(i) Obtuse vertically opposite angles

Solution:-

∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.

(ii) Adjacent complementary angles

Solution:-

∠EOA and ∠AOB are adjacent complementary angles in the given figure.

(iii) Equal supplementary angles

Solution:-

∠EOB and EOD are the equal supplementary angles in the given figure.

(iv) Unequal supplementary angles

Solution:-

∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

(v) Adjacent angles that do not form a linear pair

Solution:-

∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.

NCERT Solutions Class 7 Maths Chapter 5

Exercise 5.2

Question 1. State the property that is used in each of the following statements?

NCERT Solutions Class 7 Maths Chapter 5

(i) If a ∥ b, then ∠1 = ∠5.

Solution:-

Corresponding angles property is used in the above statement.

(ii) If ∠4 = ∠6, then a ∥ b.

Solution:-

Alternate interior angles property is used in the above statement.

(iii) If ∠4 + ∠5 = 180o, then a ∥ b.

Solution:-

Interior angles on the same side of the transversal are supplementary.

Question  2. In the adjoining figure, identify

NCERT Solutions Class 7 Maths Chapter 5

(i) The pairs of corresponding angles.

Solution:-

By observing the figure, the pairs of the corresponding angles are,

∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7

(ii) The pairs of alternate interior angles.

Solution:-

By observing the figure, the pairs of alternate interior angles are,

∠2 and ∠8, ∠3 and ∠5

(iii) The pairs of interior angles on the same side of the transversal.

Solution:-

By observing the figure, the pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8

(iv) The vertically opposite angles.

Solution:-

By observing the figure, the vertically opposite angles are,

∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8

Question 3. In the adjoining figure, p ∥ q. Find the unknown angles.

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

By observing the figure,

∠d = ∠125o … [∵ corresponding angles]

We know that Linear pair is the sum of adjacent angles is 180o

Then,

= ∠e + 125o = 180o … [Linear pair]

= ∠e = 180o – 125o

= ∠e = 55o

From the rule of vertically opposite angles,

∠f = ∠e = 55o

∠b = ∠d = 125o

By the property of corresponding angles,

∠c = ∠f = 55o

∠a = ∠e = 55o

Question 4. Find the value of x in each of the following figures if l ∥ m.

(i) 

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Let us assume the other angle on the line m be ∠y.

NCERT Solutions Class 7 Maths Chapter 5

Then,

By the property of corresponding angles,

∠y = 110o

We know that Linear pair is the sum of adjacent angles is 180o

Then,

= ∠x + ∠y = 180o

= ∠x + 110o = 180o

= ∠x = 180o – 110o

= ∠x = 70o

(ii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

By the property of corresponding angles,

∠x = 100o

5. In the given figure, the arms of the two angles are parallel.

NCERT Solutions Class 7 Maths Chapter 5

If ∠ABC = 70o, then find

(i) ∠DGC

(ii) ∠DEF

Solution:-

(i) Let us consider AB ∥ DG.

BC is the transversal line intersecting AB and DG.

By the property of corresponding angles

∠DGC = ∠ABC

Then,

∠DGC = 70o

(ii) Let us consider that BC ∥ EF.

DE is the transversal line intersecting BC and EF.

By the property of corresponding angles

∠DEF = ∠DGC

Then,

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Let us consider the two lines, l and m.

n is the transversal line intersecting l and m.

We know that the sum of interior angles on the same side of the transversal is 180o.

Then,

= 126o + 44o

= 170o

But, the sum of interior angles on the same side of transversal is not equal to 180o.

So, line l is not parallel to line m.

(ii)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,

Then, ∠x = 75o

NCERT Solutions Class 7 Maths Chapter 5

Let us consider the two lines, l and m.

n is the transversal line intersecting l and m.

We know that the sum of interior angles on the same side of the transversal is 180o.

Then,

= 75o + 75o

= 150o

But, the sum of interior angles on the same side of transversal is not equal to 180o.

So, line l is not parallel to line m.

(iii)

 

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal line n.

NCERT Solutions Class 7 Maths Chapter 5

Let us consider the two lines, l and m.

n is the transversal line intersecting l and m.

We know that the sum of interior angles on the same side of the transversal is 180o.

Then,

= 123o + ∠x

= 123o + 57o

= 180o

∴ The sum of interior angles on the same side of the transversal is equal to 180o.

So, line l is parallel to line m.

(iv)

NCERT Solutions Class 7 Maths Chapter 5

Solution:-

Let us assume ∠x be the angle formed due to the intersection of the Straight line l and transversal line n.

NCERT Solutions Class 7 Maths Chapter 5

We know that the Linear pair is the sum of adjacent angles equal to 180o.

= ∠x + 98o = 180o

= ∠x = 180o – 98o

= ∠x = 82o

Now, we consider ∠x and 72o are the corresponding angles.

For l and m to be parallel to each other, corresponding angles should be equal.

But, in the given figure, corresponding angles measure 82o and 72o, respectively.

∴ Line l is not parallel to line m.

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