# NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles is the best study material for those students who are finding difficulties in solving problems. These NCERT Solutions can help students clear doubts quickly and help in understanding the topic effectively. Students who wish to score good marks in Maths practise NCERT Solutions for Class 7 Maths.

Chapter 5 â€“ Lines and Angles of NCERT Solutions for Class 7 MathsÂ contains 2 exercises. Let us now have a quick glance at some of the topics covered in this chapter.

• Introduction to Lines and Angles
• Related angles
• Complementary Angles
• Supplementary Angles
• Linear Pair
• Vertically Opposite Angles
• Pairs of Lines
• Intersecting Lines
• Transversal
• Angles made by a Transversal
• Transversal of Parallel Lines
• Checking for Parallel Lines

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Exercise 5.1 Solutions

Exercise 5.2 Solutions

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Exercise 5.1 Page: 101

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

(i)

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 â€“ 20o

= x = 70o

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

(ii)

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 â€“ 63o

= x = 27o

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

(iii)

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 â€“ 57o

= x = 33o

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

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

(i)

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 â€“ 105o

= x = 75o

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

(ii)

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 â€“ 87o

= x = 93o

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

(iii)

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 â€“ 154o

= x = 26o

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

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

âˆ´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.

âˆ´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.

âˆ´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.

âˆ´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.

âˆ´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.

âˆ´These angles are complementary angles.

4. Find the angles 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 required angle measures is 45o.

5. Find the angles 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 required angle measures is 90o.

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

Solution:-

From the question, it is given that,

âˆ 1 and âˆ 2 are supplementary angles.

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

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

(i). Acute?

Solution:-

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

(ii). Obtuse?

Solution:-

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

(iii). Right?

Solution:-

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

âˆ´90o + 90o = 180

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 the sides,

= p + q > 45o + q

= 90o > 45o + q

= 90o â€“ 45o > q

= q < 45o

Hence, its complementary angle is less than 45o.

(i) Is âˆ 1 adjacent to âˆ 2?

Solution:-

By observing the figure we came to conclude that,

Yes, as âˆ 1 and âˆ 2 having a common vertex i.e. O and a common arm OC.

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

(ii) Is âˆ AOC adjacent to âˆ AOE?

Solution:-

By observing the figure, we came to conclude that,

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

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

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

Solution:-

By observing the figure, we came to conclude that,

Yes, as âˆ COE and âˆ EOD having a common vertex i.e. O and a common arm OE.

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

(iv) Are âˆ BOD and âˆ DOA supplementary?

Solution:-

By observing the figure, we came to conclude that,

Yes, as âˆ BOD and âˆ DOA having 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 âˆ 1 vertically opposite to âˆ 4?

Solution:-

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

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

Solution:-

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

10. Indicate which pairs of angles are:

(i) Vertically opposite angles.

Solution:-

By observing the figure we can say that,

âˆ 1 and âˆ 4, âˆ 5 and âˆ 2 + âˆ 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,

âˆ 1 and âˆ 5, âˆ 5 and âˆ 4 as these are having a common vertex and also having non common arms opposite to each other.

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

Solution:-

âˆ 1 and âˆ 2 are not adjacent angles. Because, they are not lie on the same vertex.

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

(i)

Solution:-

âˆ x = 55o, because vertically opposite angles.

âˆ x + âˆ y = 180o â€¦ [âˆµ linear pair]

= 55o + âˆ y = 180o

= âˆ y = 180o â€“ 55o

= âˆ y = 125o

Then, âˆ y = âˆ z â€¦ [âˆµ vertically opposite angles]

âˆ´ âˆ z = 125o

(ii)

Solution:-

âˆ z = 40o, because vertically opposite angles.

âˆ y + âˆ z = 180o â€¦ [âˆµ linear pair]

= âˆ y + 40o = 180o

= âˆ y = 180o â€“ 40o

= âˆ y = 140o

Then, 40 + âˆ x + 25 = 180o â€¦ [âˆµangles on straight line]

65 + âˆ x = 180o

âˆ x = 180o â€“ 65

âˆ´ âˆ x = 115o

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.

14. In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

Solution:-

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

Solution:-

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

(iii) Equal supplementary angles

Solution:-

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

(iv) Unequal supplementary angles

Solution:-

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

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

Solution:-

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

Exercise 5.2 Page: 110

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

(i) If a âˆ¥ b, then âˆ 1 = âˆ 5.

Solution:-

Corresponding angles property is used in the above statement.

(ii) If âˆ 4 = âˆ 6, then a âˆ¥ b.

Solution:-

Alternate interior angles property is used in the above statement.

(iii) If âˆ 4 + âˆ 5 = 180o, then a âˆ¥ b.

Solution:-

Interior angles on the same side of transversal are supplementary.

2. In the adjoining figure, identify

(i) The pairs of corresponding angles.

Solution:-

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

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

(ii) The pairs of alternate interior angles.

Solution:-

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

âˆ 2 and âˆ 8, âˆ 3 and âˆ 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 âˆ 2 and âˆ 5, âˆ 3 and âˆ 8

(iv) The vertically opposite angles.

Solution:-

By observing the figure, the vertically opposite angles are,

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

3. In the adjoining figure, p âˆ¥ q. Find the unknown angles.

Solution:-

By observing the figure,

âˆ d = âˆ 125o â€¦ [âˆµ corresponding angles]

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

Then,

= âˆ e + 125o = 180o â€¦ [Linear pair]

= âˆ e = 180o â€“ 125o

= âˆ e = 55o

From the rule of vertically opposite angles,

âˆ f = âˆ e = 55o

âˆ b = âˆ d = 125o

By the property of corresponding angles,

âˆ c = âˆ f = 55o

âˆ a = âˆ e = 55o

4. Find the value of x in each of the following figures if l âˆ¥ m.

(i)

Solution:-

Let us assume other angle on the line m be âˆ y,

Then,

By the property of corresponding angles,

âˆ y = 110o

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

Then,

= âˆ x + âˆ y = 180o

= âˆ x + 110o = 180o

= âˆ x = 180o â€“ 110o

= âˆ x = 70o

(ii)

Solution:-

By the property of corresponding angles,

âˆ x = 100o

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

If âˆ ABC = 70o, then find

(i) âˆ DGC

(ii) âˆ DEF

Solution:-

(i) Let us consider that AB âˆ¥ DG

BC is the transversal line intersecting AB and DG

By the property of corresponding angles,

âˆ DGC = âˆ ABC

Then,

âˆ DGC = 70o

(ii) Let us consider that BC âˆ¥ EF

DE is the transversal line intersecting BC and EF

By the property of corresponding angles,

âˆ DEF = âˆ DGC

Then,

âˆ DEF = 70o

6. In the given figures below, decide whether l is parallel to m.

(i)

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 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)

Solution:-

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

Then, âˆ x = 75o

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 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)

Solution:-

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

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 transversal is 180o.

Then,

= 123o + âˆ x

= 123o + 57o

= 180o

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

So, line l is parallel to line m.

(iv)

Solution:-

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

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

= âˆ x + 98o = 180o

= âˆ x = 180o â€“ 98o

= âˆ x = 82o

Now, we consider âˆ 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 measures 82o and 72o respectively.

âˆ´Line l is not parallel to line m.

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## Frequently Asked Questions on NCERT Solutions for Class 7 Maths Chapter 5

### How NCERT Solutions for Class 7 Maths Chapter 5 helpful for board exams?

NCERT Solutions for Class 7 Maths Chapter 5 provides answers with detailed descriptions as per term limit particularised by the Board for self-evaluation. Solving these solutions will provide excellent practice for the students so they can finish the paper on time. So, itâ€™s clear that the NCERT Solutions for Class 7 Maths Chapter 5 are essential to score high in examinations. Students can get acquainted with writing exams and will be able to face exams more confidently.

### Mention the topics that are covered in NCERT Solutions for Class 7 Maths Chapter 5?

The topics that are covered in NCERT Solutions for Class 7 Maths Chapter 5 are
1. Introduction to Lines and Angles
2. Related angles
3. Complementary Angles
4. Supplementary Angles
6. Linear Pair
7. Vertically Opposite Angles
8. Pairs of Lines
9. Intersecting Lines
10. Transversal
11. Angles made by a Transversal
12. Transversal of Parallel Lines
13. Checking for Parallel Lines.

### Is it necessary to practice all the exercises present in Chapter 5 of NCERT Solutions for Class 7 Maths?

Yes, it is compulsory to practice all the exercises present in Chapter 5 of NCERT Solutions for Class 7 Maths. Because all exercises contain numerous questions to solve which may come in their finals. This makes them more confident towards the syllabus they have.

#### 1 Comment

1. AAKANKSHA DAS

nice paper covered all sums!!!!!!!!!!!!!