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NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles -Download PDF

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles -Download PDF

Edited By Ramraj Saini | Updated on Feb 07, 2024 05:09 PM IST

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles - Topics like how to identify different lines, line segments, and angles in the shapes are dealt with in NCERT of Class 6. In this chapter, we deal with lines, different kinds of angles and their measurements. The solutions of NCERT maths chapter 5 lines and angles class 7 give an explanation to all these questions. These NCERT Solutions are given here with a step-by-step explanation of each and every problem of NCERT textbook. In this chapter students are always confused between a line, a ray and a line-segment. So, let's discuss each term one by one- A line segment has two endpoints. If we extend these two endpoints in either direction endlessly, we get a line.

In the NCERT solutions for Class 7 Maths chapter 5 lines and angles, we will study questions related to different kinds of angles like complementary angles, adjacent angles, supplementary angles, vertically opposite angles; pairs of lines like intersecting lines, transversal and many more. Here you will get NCERT Solutions for Class 7 . Before going through the solutions, it is advisable that students must refer to the NCER Class 7 Maths Syllabus and know the exam pattern and important topics.

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7- Important Formulae

Complementary angles: ∠A + ∠B = 90°

Supplementary angles: ∠A + ∠B = 180°

Linear pair: ∠1 + ∠2 = 180°

If two parallel lines are intersected by a transversal line then:

  • Pairs of alternate interior or exterior angles are equal
  • Pairs of corresponding angles are equal
  • Interior angles on the same side of the transversal are supplementary

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 - Important Points

Following are some important points discussed in lines and angles class 7.

Complementary angles: Angles ∠A and ∠B are complementary if their measures add up to 90 degrees.

Supplementary angles: Angles ∠A and ∠B are supplementary if their measures add up to 180 degrees.

Adjacent angles: Have a common vertex and a common arm but no common arm on either side of the common arm.

Linear pair: It is a pair of the adjacent angles whose non-common sides are opposite rays and the sum of both angles are 180°.

Vertically opposite angles: When two lines are intersected, vertically opposite angles formed are equal.

If two parallel lines are intersected by a transversal line then,

Pairs of alternate interior or exterior angles are equal.

Pairs of corresponding angles are equal.

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

Free download NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles PDF for CBSE Exam.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

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NCERT Solutions for Class 7 Maths Chapter 5 Questions and Exercise

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.2.1

1. Can two acute angles be a complement to each other?

Answer: Yes, two acute angles can be complementary to each other.

For e.g. Acute angles 20^{\circ} and 70^{\circ} are complementary angle as their sum is 90^{\circ} .

2. Can two obtuse angles be complement to each other?

Answer:

Since obtuse angles are greater than 90^{\circ} . Thus two obtuse angles cannot be a complement to each other. (as the sum of complementary angles is 90^{\circ} .)

3. Can two right angles be complement to each other?

Answer: The sum of angles in complementary angles is 180^{\circ} . Thus two right angles cannot be complementary to each other.

1.(i) Which pairs of following angles are complementary?

01

Answer: Sum of the angles in the given figure is : =\ 70^{\circ}\ +\ 20^{\circ}\ =\ 90^{\circ}

Thus two angles are complementary to each other.

1.(ii) Which pairs of following angles are complementary?

1643866616640

Answer: The sum of the two angles is : =\ 75^{\circ}\ +\ 25^{\circ}\ =\ 100^{\circ}

In complementary angles sum of the angles is 90^{\circ} . Hence given pair of angles are not complementary.

1. (iii) Which pairs of the following angles are complementary?

1643866657060

Answer: We know that the sum angles of complementary angles is 90^{\circ} .

In the given figure: Sum of angles is =\ 48^{\circ}\ +\ 52^{\circ}\ =\ 100^{\circ}

Hence given pair of angles are not complementary.

1.(iv) Which pairs of following angles are complementary?

1643866693169

Answer: The sum of the two angles is : =\ 35^{\circ}\ +\ 55^{\circ}\ =\ 90^{\circ}

In complementary angles sum of the angles is 90^{\circ} . Hence given pair of angles are complementary to each other.

2 .(i) What is the measure of the complement of each of the following angles?

(i)45^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Thus the complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 45^{\circ}\ =\ 45^{\circ}

2.(ii) What is the measure of the complement of each of the following angles?

(ii)65^{o}

Answer: The sum of complementary angles are 90^{\circ} .

Thus the required angle is : =\ 90^{\circ}\ -\ 65^{\circ}\ =\ 25^{\circ}

2.(iii) What is the measure of the complement of each of the following angles?

(iii)41^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Hence the required complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 41^{\circ}\ =\ 49^{\circ}

2.(iv) What is the measure of the complement of each of the following angles?

(iv)54^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Hence the complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 54^{\circ}\ =\ 36^{\circ}

3. The difference in the measures of two complementary angles is 12^{o} . Find the measures of the angles.

Answer: Let one of the angles be \Theta .

It is given that the angles are complementary to each other. So the other angle will be 90^{\circ}\ -\ \Theta .

Further, it is given that the difference of the angle is 12.

So the equation is : 90^{\circ}\ -\ \Theta\ -\ \Theta\ =\ 12^{\circ}

or 2\Theta\ =\ 90^{\circ}\ -\ 12^{\circ}

or \Theta\ =\ 39^{\circ}

Hence the two angles are 39^{\circ} and 51^{\circ} .

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.2

1. Can two obtuse angles be supplementary?

Answer: No, two obtuse angles cannot be supplementary as their the sum of angles will exceed 180^{\circ} .

2. Can two acute angles be supplementary?

Answer: No two acute angles cannot be supplementary.

For being the supplementary angles their sum should be 180^{\circ} .

But the acute angles are less than 90^{\circ} . Hence their maximum doesn't reach 180^{\circ} .

3. Can two right angles be supplementary?

Answer: Yes, two right angles are supplementary as their sum is 180^{\circ} .

1. Find the pairs of supplementary angles in Fig : 1643866724771

Answer: We know that the sum of the supplementary angle is 180^{\circ} .

(i) Sum of the angles is : =\ 110^{\circ}\ +\ 50^{\circ}\ =\ 160^{\circ} . Hence the angles are not supplementary.

(ii) Sum of the angles is : =\ 105^{\circ}\ +\ 65^{\circ}\ =\ 170^{\circ} . Thus the angles are not supplementary.

(iii) Sum of the angles is : =\ 50^{\circ}\ +\ 130^{\circ}\ =\ 180^{\circ} . Hence the angles are supplementary to each other.

(iv) Sum of the angles is : =\ 45^{\circ}\ +\ 45^{\circ}\ =\ 90^{\circ} . Thus the angles are not supplement to each other.

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.3

1. Can two adjacent angles be supplementary?

Answer: Yes, two adjacent angles can be supplementary.

For e.g., 40^{\circ} and 140^{\circ} can be two adjacent angles which are supplementary angles.

2. Can two adjacent angles be complementary?

Answer: Yes, two adjacent angles can be complementary to each other.

For e.g., adjacent angles 40^{\circ} and 50^{\circ} are complementary angles.

3. Can two obtuse angles be adjacent angles?

Answer: Yes, two obtuse angles can be adjacent for e.g., 100^{\circ} and 150^{\circ} can be adjacent angles.

4. Can an acute angle be adjacent to an obtuse angle?

Answer: Yes, the acute angle can be adjacent to an obtuse angle.

For e.g., 20^{\circ} and 120^{\circ} can be adjacent angles.

1. Are the angles marked 1 and 2 adjacent? (Fig). If they are not adjacent, say, ‘why’.

02

Answer: The condition for being adjacent angles are:-

(a) they have a common vertex

(b) they have common arm

Hence in the given figures:-

(i) These angles are adjacent angles as they agree above conditions.

(ii) The angles are adjacent angles.

(iii) These angles are not adjacent as their vertices are different.

(iv) These are adjacent angles.

(v) The angles are adjacent angles.

2. In the given Fig , are the following adjacent angles?

(a) \angle AOB and \angle BOC
(b) \angle BOD and \angle BOC

Justify your answer.

03

Answer: (a) \angle AOB and \angle BOC are adjacent angles as they have common vertex and share a common arm.

(b) \angle BOD and \angle BOC are not adjacent angles as \angle BOC is contained in \angle BOD .

NCERT Solutions for C lass 7 Maths Chapter 5 Lines and Angles Topic 5.2.4

1. Can two acute angles form a linear pair?

Answer: No two acute angles cannot form a linear pair. As the sum of angles in the linear pair is 180^{\circ} .

But the acute angles have their maximum value of 90^{\circ} thus their sum cannot be 180^{\circ} .

2. Can two obtuse angles form a linear pair?

Answer: No two obtuse angles cannot form a linear pair as their sum will exceed 180^{\circ} , but the sum of angles in linear pair is 180^{\circ} .

3. Can two right angles form a linear pair?

Answer: Yes, two right angles will form a linear pair as their sum is 180^{\circ} which is the sum of angles in linear pair.

1. Check which of the following pairs of angles form a linear pair (Fig):

1643866798868

Answer: The sum angles of linear pair is 180^{\circ} .

(i) Sum of the given angles is : =\ 40^{\circ}\ +\ 140^{\circ}\ =\ 180^{\circ} . Thus these are linear pair.

(ii) Sum of the given angles is : =\ 60^{\circ}\ +\ 60^{\circ}\ =\ 120^{\circ} . Thus these are not linear pair.

(iii) Sum of the given angles is : =\ 90^{\circ}\ +\ 80^{\circ}\ =\ 170^{\circ} . Thus these are not a linear pair.

(iv) Sum of the given angles is : =\ 115^{\circ}\ +\ 65^{\circ}\ =\ 180^{\circ} . Thus these are linear pair.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.2.5

1. In the given figure, if \angle 1=30^{o} , find \angle 2 and \angle 3 .

1643866863659

Answer: From the given figure :

(a) \angle 1\ =\ \angle 3\ =\ 30^{\circ} (Vertically opposite angles)

(b) \angle 2\ =\ 180^{\circ}\ -\ \angle 1\ =\ 150^{\circ} (Linear pair)

2. Give an example for vertically opposite angles in your surroundings.

Answer: The very common example of vertically opposite angle is scissors. Its arms form vertically opposite angles.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.1

1. Find examples from your surroundings where lines intersect at right angles.

Answer: The floor and the pillars in the house are at the right angle. Apart from this, the walls are perpendicular to the floor.

3. Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

Answer: We know that the opposite sides of the rectangle are equal and parallel to each other.

Then for two interior angles on the same side of the transversal, we can write :

\angle A\ +\ \angle B\ =\ 180^{\circ}

Also, \angle A\ =\ \angle B (Since opposite sides are equal)

Thus \angle A\ =\ \angle B\ =\ 90^{\circ}

4. If two lines intersect, do they always intersect at right angles?

Answer: No, it is not necessary that lines always intersect at right angles. The lines may form an acute angle (another angle will be obtuse as to form a linear pair).

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.2

1. Suppose two lines are given. How many transversals can you draw for these lines?

Answer: We can draw infinite transversals from these two lines.

2. If a line is a transversal to three lines, how many points of intersections are there?

Answer: We know that transversal cuts lines at distinct points. Thus if a transversal cuts 3 lines then it will have 3 intersecting points.

3. Try to identify a few transversals in your surroundings.

Answer: Few examples of the transversal are road crossing of different railway line crossing the other lines. Transversal intersects lines at a distinct point.

1.(i) Name the pairs of angles in each figure:

1643866903425

(i)

Answer: The given pair of angles are corresponding angles.

1.(ii) Name the pairs of angles in each figure:

1643866941544

(ii)

Answer: The given pair of angles are alternate interior angles.

1.(iii) Name the pairs of angles in each figure:

015

Answer: The angles shown are pair of interior angles.

1.(iv) Name the pairs of angles in each figure:

017

Answer: These are a pair of corresponding angles.

1.(v) Name the pairs of angles in each figure:

1643866978318

(v)

Answer: The angles shown are pair of alternate interior angles.

1.(vi) Name the pairs of angles in each figure:

020

Answer: The given angles are linear pairs of angles as they form a straight line.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1

1.(i) Find the complement of each of the following angles:

04

Answer: The sum of the complementary angle is 90^{\circ} .

Thus the complementary angle to the given angle is : =\ 90^{\circ}\ -\ 20^{\circ}\ =\ 70^{\circ}

1.(ii) Find the complement of each of the following angles:

05

Answer: The sum of the complementary angle is 90^{\circ} .

Thus the complementary angle to the given angle is : =\ 90^{\circ}\ -\ 63^{\circ}\ =\ 27^{\circ}

1.(iii) Find the complement of each of the following angles:

06

Answer: The sum of the complement angles is 90^{\circ} .

Thus the complement of the angle is given by : =\ 90^{\circ}\ -\ 57^{\circ}\ =\ 33^{\circ}

2.(i) Find the supplement of each of the following angles:

014

Answer: We know that sum of supplement angles is 180^{\circ}

The supplement of the given angle is : =\ 180^{\circ}\ -\ 105^{\circ}\ =\ 75^{\circ}

2.(ii) Find the supplement of each of the following angles:

1643867078109

Answer: We know that the sum of angles of supplementary pair is 180^{\circ} .

Thus the supplement of the given angle is : =\ 180^{\circ}\ -\ 87^{\circ}\ =\ 93^{\circ}

2.(iii) Find the supplement of each of the following angles:

1643867109355

Answer: We know that the sum of angles of supplementary pair is 180^{\circ} .

Thus the supplement of the given angle is :

=\ 180^{\circ}\ -\ 154^{\circ}\ =\ 26^{\circ}


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

(i) 65^{o},115^{o} (ii) 63^{o}, 27^{o} (iii) 112^{o}, 68^{o}

(iv) 130^{o}, 50^{o} (v) 45^{o}, 45^{o} (vi) 80^{o}, 10^{o}

Answer: We know that the sum of supplementary angles is 180^{\circ} and the sum of complementary angle is 90^{\circ} .

(i) Sum of the angles is : 65^{\circ}\ +\ 115^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(ii) Sum of the angles is : 63^{\circ}\ +\ 27^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

(iii) Sum of the angles is : 112^{\circ}\ +\ 68^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(iv) Sum of the angles is : 130^{\circ}\ +\ 50^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(v) Sum of the angles is : 45^{\circ}\ +\ 45^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

(vi) Sum of the angles is : 80^{\circ}\ +\ 10^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

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

Answer: Let the required angle be \Theta .

Then according to question, we have :

\Theta\ +\ \Theta\ =\ 90^{\circ}

or 2\Theta\ =\ 90^{\circ}

or \Theta\ =\ 45^{\circ}

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

Answer: Let the required angle be \Theta .

Then according to the question :

\Theta\ +\ \Theta \ =\ 180^{\circ}

or 2\Theta \ =\ 180^{\circ}

or \Theta \ =\ 90^{\circ}

Hence the angle is 90^{\circ} .

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

013

Answer: Since it is given that \angle 1 and \angle 2 are supplementary angles, i.e. the sum of both angles is 180^{\circ} .

Thus if \angle 1 is decreased then to maintain the sum \angle 2 needs to be increased.

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

(i) acute ? (ii) obtuse ? (iii) right ?

Answer: We know that the sum of supplementary angles is 180^{\circ} .

(i) The maximum value of the sum of two acute angles is less than 180^{\circ} . Thus two acute angles can never be supplementary.

(ii) The minimum value of the sum of two obtuse angles is more than 180^{\circ} . Thus two obtuse angles can never be supplementary.

(iii) Sum of two right angles is 180^{\circ} . Hence two right angles are supplementary.

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: We know that the sum of two complementary angles is 90^{\circ} .

Thus if one of the angles is greater than 45^{\circ} then the other angle needs to be less than 45^{\circ} .

9. In the adjoining figure:

(i) Is \angle 1 adjacent to \angle 2 ?
(ii) Is \angle AOC adjacent to \angle AOE ?

(iii) Do \angle COE and \angle EOD form a linear pair?
(iv) Are \angle BOD and \angle DOA supplementary?
(v) Is \angle 1 vertically opposite to \angle 4 ?
(vi) What is the vertically opposite angle of \angle 5 ?

012

Answer: (i) Yes, \angle 1 adjacent to \angle 2 as these have the same vertex and have one common arm.

(ii) No, \angle AOC is not adjacent to \angle AOE . This is because \angle AOE contains \angle AOC .

(iii) Yes the given angles form a linear pair as they are pair of supplementary angles.

(iv) Since BOA is a straight line thus the given angles are supplementary.

(v) Yes, \angle 1 and \angle 4 are vertically opposite angles as they are the angles formed by two intersecting straight lines.

(vi) The vertically opposite angle to \angle 5 is \left ( \angle 2\ +\ \angle 3 \right ) .

10. (i) Indicate which pairs of angles are:

(i) Vertically opposite angles.

023

Answer: The vertically opposite pairs are :

(a) \angle 1 and \angle 4

(b) \angle 5 and \left ( \angle 2\ +\ \angle 3 \right )

10.(ii) Indicate which pairs of angles are:

(ii) Linear pairs

010

Answer: The sum of angles in linear pair is 180^{\circ} .

Thus the linear pairs are :

(a) \angle 1\ and\ \angle 5

(b) \angle 4\ and\ \angle 5

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

011

Answer: No, \angle 1 and \angle 2 are not adjacent angles as their vertex is not same/common.

For being adjacent angles the pair must have a common vertex and have a common arm.


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

09

Answer: From the figure :

(i) \angle x\ =\ 55^{\circ} (Vertically opposite angle)

(ii) \angle y\ =\ 180^{\circ}\ -\ 55^{\circ}\ =\ 125^{\circ} (Linear pair)

(iii) \angle y\ =\ \angle z\ =\ 125^{\circ} (Vertically opposite angle)

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

1643867159703

Answer: From the figure we can observe that :

(i) \angle z\ =\ 40^{\circ} (Vertically opposite angle)

(ii) \angle x\ =\ 180^{\circ}\ -\ 40^{\circ}\ -\ 25^{\circ}\ =\ 115^{\circ} (Linear pair/straight line)

(iii) \angle y\ =\ 180^{\circ}\ -\ \angle z\ =\ 140^{\circ} (Vertically opposite angle).

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) 90^{\circ}

(ii) 180^{\circ}

(iii) Supplementary angles

(iv) Straight line

(v) equal

(vi) obtuse angles (as they form a line).

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

08

Answer: (i) \angle AOD\ and\ \angle BOC are the vertically obtuse angles.

(ii) \angle AOB\ and\ \angle AOE are the complementary angles.

(iii) \angle BOE\ and\ \angle DOE are the equal supplementary angles.

(iv) \angle BOC\ and\ \angle COD are the unequal pair of supplementary angle.

(v) \angle AOB\ and\ \angle AOE , \angle EOD\ and\ \angle COD and \angle AOE\ and\ \angle EOD are adjacent angles but are not supplementary angles.


NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

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

(i) If a\parallel b , then \angle 1= \angle 5 .

07

Answer: The statement "If a\parallel b , then \angle 1= \angle 5 " is true using the corresponding angles property .

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

(ii) If \angle 4=\angle 6 , then a\parallel b.

07

Answer: The property used here is 'alternate interior angle property'.

(iii) If \angle 4+\angle 5= 180^{o} , then a\parallel b.
07

Answer: The property used here is ' Interior angles on the same side of the transversal are a pair of supplementary angles '.


2. 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.

016


Answer: (i) Corresponding angles :- \angle 1\ and\ \angle 5 , \angle 2\ and\ \angle 6 , \angle 3\ and\ \angle 7 , \angle 4\ and\ \angle 8

(ii) Alternate interior angles :- \angle 2\ and\ \angle 8 , \angle 3\ and\ \angle 5 ,

(iii) Alternate angles on the same side of traversal :- \angle 2\ and\ \angle 5 , \angle 3\ and\ \angle 8

(iv) Vertically opposite angles :- \angle 1\ and\ \angle 3 , \angle 2\ and\ \angle 4 , \angle 5\ and\ \angle 7 , \angle 6\ and\ \angle 8

3. In the adjoining figure, p\parallel q . Find the unknown angles.

018

Answer: The angles can be found using different properties:

(a) \angle e\ =\ 180^{\circ}\ -\ 125^{\circ}\ =\ 55^{\circ} (The angles are linear pair)

(b) \angle e\ =\ \angle f\ =\ 55^{\circ} (Vertically opposite angle)

(c) \angle d\ =\ 125^{\circ} (Corresponding angle)

(d) \angle d\ =\ \angle b\ =\ 125^{\circ} (Vertically opposite angle)

(e) \angle a\ =\ \angle c\ =\ 180^{\circ}\ -\ 125^{\circ}\ =\ 55^{\circ} (Vertically opposite angel, linear pair).

4.(i) Find the value of x in each of the following figures if l\parallel m .

019

Answer: The linear pair of the 110^{\circ} is : \Theta \ =\ 180^{\circ}\ -\ 110^{\circ}\ =\ 70^{\circ}

Thus the value of x is : x\ =\ 70^{\circ} (Corresponding angles of parallel lines are equal).

4.(ii) Find the value of x in each of the following figures if l\parallel m.

021

Answer: The value of x is 100^{\circ} , as these are the corresponding angles.

5. In the given figure, the arms of two angles are parallel. If \angle ABC= 70^{o} , then find

(i) \angle DGC

(ii)\angle DEF

022

Answer: (i) Since side AB is parallel to DG.

Thus : \angle DGC\ =\ 70^{\circ} (Corresponding angles of parallel arms are equal.)

(ii) Further side BC is parallel to EF.

We have : \angle DEF\ =\ \angle DGC\ =\ 70^{\circ} (Corresponding angles of parallel arms are equal.)

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

1643867198020 Answer: (i) In this case. the sum of the interior angle is 126^{\circ}\ +\ 44^{\circ}\ =\ 170^{\circ} thus l is not parallel to m.\

(ii) In this case, also l is not parallel to m as the corresponding angle cannot be 75^{\circ} (Linear pair will not form).

(iii) In this l and m are parallel. This is because the corresponding angle is 57^{\circ} and it forms linear pair with 123^{\circ} .

(iv) The lines are not parallel as the linear pair not form. (Since the corresponding angle will be 72^{\circ} otherwise.)

Lines and Angles Class 7 Maths Chapter 5-Topics

  • Related Angles
  • Pairs Of Lines
  • Checking For Parallel Lines

NCERT Solutions for Class 7 Maths Chapter Wise

Chapter No.

Chapter Name

Chapter 1

Integers

Chapter 2

Fractions and Decimals

Chapter 3

Data Handling

Chapter 4

Simple Equations

Chapter 5

Lines and Angles

Chapter 6

The Triangle and its Properties

Chapter 7

Congruence of Triangles

Chapter 8

Chapter 9

Rational Numbers

Chapter 10

Practical Geometry

Chapter 11

Perimeter and Area

Chapter 12

Algebraic Expressions

Chapter 13

Exponents and Powers

Chapter 14

Symmetry

Chapter 15

NCERT Solutions for Class 7 Subject Wise

Benefits of NCERT solutions for Class 7 Maths chapter 5 Lines and Angles:

  • Solving homework is an easy task with solutions of NCERT Class 7 Maths chapter 5 Lines and Angles in hand.
  • Questions of similar type from CBSE NCERT solutions for Class 7 Maths chapter 5 are expected for the Class exams.
  • Practice all the questions from NCERT solutions for Class 7 Maths chapter 5 Lines and Angles to score well in the exam.

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. Why we study lines and angles?

Lines and angles which are discussed in chapter 5 maths class 7 are the basics of geometry. It will be definitely useful in higher studies. Not only in mathematics but in almost all the subjects. Students can download lines and angles class 7 pdf to study both online and offline. 

2. What are the topics covered in NCERT Class 7 Maths Chapter 5

Here are the topics are covered in NCERT solution Class 7 chapter 5

  • Related Angles
  • Pairs Of Lines 
  • Checking For Parallel Lines

Students can study lines and angles class 7 pdf  both online and offline. 

3. Write the different types of angles

Following is a list of different types of angles that are discussed in NCERT Maths class 7 chapter 5  

  • Acute Angles.
  • Obtuse Angles.
  • Right Angles.
  • Straight Angles.
  • Reflex Angles.
  • Full Rotation.

Students can find these concepts in lines and angles class 7 pdf which can be downloaded form official website of Careers360.

4. What are complementary and supplementary angles discussed in NCERT maths class 7 chapter 5

According to NCERT maths class 7 chapter 5:

  • Complementary angles are two angles whose sum is 90 degrees. In other words, they "complete" each other to form a right angle.
  • Supplementary angles are two angles whose sum is 180 degrees. They form a straight line when placed next to each other.
5. What's the difference between adjacent and linear pairs of angles?

According to chapter 5 class 7 maths the difference between adjacent and linear pairs of angles is:

  • Adjacent angles share a common vertex and a common side but don't overlap. They are side by side.
  • Linear pairs are adjacent angles that form a straight line when combined. The sum of their measures is always 180 degrees.

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20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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