NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Question

Here you will find NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles, which will assist you in understanding the important concepts covered in the chapter and completing your homework on time. With the help of these Chapter 5 NCERT Solutions, you can improve the quality of your studies while also making it easier to solve the difficulties that lie ahead.

This chapter 5 Class 7 Maths textbook contains a variety of concepts that will help you develop the necessary skills to solve more and more questions not only in this class 7 but also in upcoming board exams. It will introduce a new set of topics that will help you better understand geometry. These NCERT Solutions will provide a good experience and provide opportunities to learn new things.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles contains questions and answers about the chapter Lines and Angles. This topic introduces you to basic geometry, with a focus on the properties of the angles formed.  (i) when two lines intersect and (ii) when a line intersects two or more parallel lines at distinct points. This chapter is part of the Unit - of geometry and is covered in the CBSE Syllabus for Class 9 Math.

Answer 1

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

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

Answer:

(i) Complement of 20° = 90° – 20° = 70°

(ii) Complement of 63° = 90° – 63° = 27°

(iii) Complement of 57° = 90° – 57° = 33°

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

Answer:

(i) Supplement of 105° = 180° – 105° = 75°

(ii) Supplement of 87° = 180° – 87° = 93°

(iii) Supplement of 154° = 180° – 154° = 26°

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

(i) 65°, 115°

(ii) 63°, 27°

(iii) 112°, 68°

(iv) 130°, 50°

(v) 45°, 45°

(v) 45°, 45°

Answer:

(i) 65^o, 115^o

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

Then,

= 65^o + 115^o

= 180^o

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

∴ These angles are supplementary angles.

(ii) 63^o, 27^o

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

Then,

= 63^o + 27^o

= 90^o

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

∴ These angles are complementary angles.

(iii) 112^o, 68^o

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

Then,

= 112^o + 68^o

= 180^o

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

∴ These angles are supplementary angles.

(iv) 130^o, 50^o

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

Then,

= 130^o + 50^o

= 180^o

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

∴ These angles are supplementary angles.

(v) 45^o, 45^o

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

Then,

= 45^o + 45^o

= 90^o

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

∴ These angles are complementary angles.

(vi) 80^o, 10^o

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

Then,

= 80^o + 10^o

= 90^o

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

∴ These angles are complementary angles.

4. Find the angles which are equal to their complement.

Answer:

Let the measure of the required angle be x^o.

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

Then,

= x + x = 90^o

= 2x = 90^o

= x = 90/2

= x = 45^o

Hence, the required angle measure is 45^o.

5. Find the angles which are equal to their supplement.

Answer:

Let the measure of the required angle be x^o.

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

Then,

= x + x = 180^o

= 2x = 180^o

= x = 180/2

= x = 90^o

Hence, the required angle measure is 90^o.

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?

Answer:

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.

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

(i) Acute?

(ii) Obtuse?

(iii) Right?

Answer:

(i) No. If two angles are acute, which means less than 90^o, then they cannot be supplementary because their sum will always be less than 90^o.

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

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

∴ 90^o + 90^o = 180^o

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

Answer:

Let us assume the complementary angles be p and q,

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

Then,

= p + q = 90^o

It is given in the question that p > 45^o

Adding q on both sides,

= p + q > 45^o + q

= 90^o > 45^o + q

= 90^o – 45^o > q

= q < 45^o

Hence, its complementary angle is less than 45^o.

Answer 2

9. In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?

(ii) Is ∠AOC adjacent to ∠AOE?

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

(iv) Are ∠BOD and ∠DOA supplementary?

(v) Is ∠1 vertically opposite to ∠4?

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

Answer:

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

(vi) ∠COB is the vertically opposite angle of ∠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.

(ii) Linear pairs.

Answer:

(i) 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) 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.

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

Answer:

∠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) 

(ii)

Answer:

(i) ∠x = 55^o, because vertically opposite angles.

∠x + ∠y = 180^o … [∵ linear pair]

= 55^o + ∠y = 180^o

= ∠y = 180^o – 55^o

= ∠y = 125^o

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

∴ ∠z = 125^o

(ii) ∠z = 40^o, because vertically opposite angles.

∠y + ∠z = 180^o … [∵ linear pair]

= ∠y + 40^o = 180^o

= ∠y = 180^o – 40^o

= ∠y = 140^o

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

65 + ∠x = 180^o

∠x = 180^o – 65

∴ ∠x = 115^o

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 __________.

Answer:

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

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

(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.

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

Answer:

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

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

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

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

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

Answer 3

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

(i) If a ∥ b, then ∠1 = ∠5.

(ii) If ∠4 = ∠6, then a ∥ b.

(iii) If ∠4 + ∠5 = 180^o, then a ∥ b.

Answer:

(i) Corresponding angles property is used in the above statement.

(ii) Alternate interior angles property is used in the above statement.

(iii) Interior angles on the same side of the transversal are supplementary.

16. 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.

Answer:

(i) By observing the figure, the pairs of the corresponding angles are,

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

(ii) By observing the figure, the pairs of alternate interior angles are,

∠2 and ∠8, ∠3 and ∠5

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

(iv) By observing the figure, the vertically opposite angles are,

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

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

Answer:

By observing the figure,

∠d = ∠125^o … [∵ corresponding angles]

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

Then,

= ∠e + 125^o = 180^o … [Linear pair]

= ∠e = 180^o – 125^o

= ∠e = 55^o

From the rule of vertically opposite angles,

∠f = ∠e = 55^o

∠b = ∠d = 125^o

By the property of corresponding angles,

∠c = ∠f = 55^o

∠a = ∠e = 55^o

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

(i)

 

(ii)

Answer:

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

Then,

By the property of corresponding angles,

∠y = 110^o

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

Then,

= ∠x + ∠y = 180^o

= ∠x + 110^o = 180^o

= ∠x = 180^o – 110^o

= ∠x = 70^o

(ii) By the property of corresponding angles,

∠x = 100^o

Answer 4

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

If ∠ABC = 70^o, then find

(i) ∠DGC

(ii) ∠DEF

Answer:

(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 = 70^o

(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,

∠DEF = 70^o

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

(i)

(ii)

(iii)

(iv)

Answer:

(i) 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 180^o.

Then,

= 126^o + 44^o

= 170^o

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

So, line l is not parallel to line m.

(ii)

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

Then, ∠x = 75^o

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 180^o.

Then,

= 75^o + 75^o

= 150^o

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

So, line l is not parallel to line m.

(iii) Let us assume ∠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 the transversal is 180^o.

Then,

= 123^o + ∠x

= 123^o + 57^o

= 180^o

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

So, line l is parallel to line m.

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

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

= ∠x + 98^o = 180^o

= ∠x = 180^o – 98^o

= ∠x = 82^o

Now, we consider ∠x and 72^o 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 82^o and 72^o, respectively.

∴ Line l is not parallel to line m.