NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

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.

Latest: NCERT Class 7 Maths: Chapterwise Important Formulas with Examples and Points

This Story also Contains

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7- Important Formulae
NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 - Important Points
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles
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
NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.2
NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.3
NCERT Solutions for C lass 7 Maths Chapter 5 Lines and Angles Topic 5.2.4
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.2.5
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.1
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.2
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2
Lines and Angles Class 7 Maths Chapter 5-Topics

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

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

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?

Answer: Sum of the angles in the given figure is :

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’.

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.

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:

Answer: The angles shown are pair of interior angles.

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

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:

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:

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:

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:

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:

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.

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 $\angle 5$ ?

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 .

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

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

(ii) Linear pairs

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.

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:

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:

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

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 $\angle 1= \angle 5$ .

Answer: The statement "If , then " 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 $a\parallel b.$

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

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

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

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.

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.

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)

(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 $l\parallel m.$

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	Comparing quantities
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	Visualising Solid Shapes

NCERT Solutions for Class 7 Subject Wise

NCERT Solutions for Class 7 Maths

NCERT Solutions for Class 7 Science

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 Questions (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.

Also Read

NCERT Solutions for Class 7 Science Chapter 18 Wastewater Story

NCERT Solutions for Class 7 Science Chapter 17 Forests Our Lifeline

NCERT Solutions for Class 7 Science Chapter 16 Water A Precious Resource

NCERT Solutions for Class 7 Science Chapter 14 Electric Current and Its Effects

NCERT Solutions for Class 7 Science Chapter 13 Motion and Time

NCERT Solutions for Class 7 Science Chapter 12 Reproduction in Plants

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

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 .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

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.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

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

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

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

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

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

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

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

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

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

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

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Lines and Angles Class 7 Maths Chapter 5-Topics

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