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

**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 class 7 maths chapter 5 lines and angles 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 always confuse 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.

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**Important points of NCERT Class 7 Maths Chapter 5 Lines and Angles **

Problems related to the following points are discussed in the NCERT solutions for class 7 maths chapter 5 lines and angles.

- An angle is formed when two lines or line-segments or rays meet

Pairs of Angles | Condition |

Two complementary angles | Measures add up to |

Two supplementary angles | Measures add up to |

Two adjacent angles | Have a common arm and a common vertex but no common interior |

Linear pair | Adjacent and supplementary |

- When two lines l and m are intersected it means they both are meet at a point and the meeting point is called the point of intersection.
- When two lines l and m drawn on a sheet of paper do not meet or intersect, however far produced, then this lines called as parallel lines.
- When two lines intersect we have two pairs of opposite angles. They are called vertically opposite angles and both angles are equal in measure.
- Transversal- It is a line that intersects two or more than two lines at distinct points. And it gives rise to several types of angles. For example interior angles, exterior angles, corresponding angles, alternate interior, and alternate exterior angles.

Topic-wise questions are also explained in the CBSE NCERT solutions for class 7 maths chapter 5 lines and angles.

## **Topics of NCERT Grade 7 Maths Chapter 5 Lines and Angles**

5.1 Introduction

5.2 Related Angles

5.2.1 Complementary Angles

5.2.2 Supplementary Angles

5.2.3 Adjacent Angles

5.2.4 Linear Pair

5.2.5 Vertically Opposite Angles

5.3 Pairs of Lines

5.3.1 Intersecting Lines

5.3.2 Transversal

5.3.3 Angles made by a Transversal

5.3.4 Transversal of Parallel Lines

5.4 Checking for Parallel Lines

**NCERT ****Solutions for** class 7 maths chapter 5 lines and angles topic 5.2.1

**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 and are complementary angle as their sum is .

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

** Answer: **

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

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

** Answer: **The sum of angles in complementary angles is . 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?

** Answer: **The sum of the two angles is :

In complementary angles sum of the angles is . Hence given pair of angles are not complementary.

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

** Answer:** We know that the sum angles of complementary angles is .

In the given figure: Sum of angles is

Hence given pair of angles are not complementary.

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

**Answer: **The sum of the two angles is :

In complementary angles sum of the angles is . 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?

**Answer: **We know that the sum of complementary angles is .

Thus the complement of the given angle is :

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

**Answer: **The sum of complementary angles are .

Thus the required angle is :

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

**Answer: **We know that the sum of complementary angles is .

Hence the required complement of the given angle is :

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

**Answer: **We know that the sum of complementary angles is .

Hence the complement of the given angle is :

** 3. ** The difference in the measures of two complementary angles is . Find the measures of the angles.

**Answer: **Let one of the angles be .

It is given that the angles are complementary to each other. So the other angle will be .

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

So the equation is :

or

or

Hence the two angles are and .

**NCERT solutions for class 7 maths chapter 5 lines and angles 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 .

** 2. ** Can two acute angles be supplementary?

** Answer: **No two acute angles cannot be supplementary.

For being the supplementary angles their sum should be .

But the acute angles are less than . Hence their maximum doesn't reach .

** 3. ** Can two right angles be supplementary?

** Answer: **Yes, two right angles are supplementary as their sum is .

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

**Answer: **We know that the sum of the supplementary angle is .

(i) Sum of the angles is : . Hence the angles are not supplementary.

(ii) Sum of the angles is : . Thus the angles are not supplementary.

(iii) Sum of the angles is : . Hence the angles are supplementary to each other.

(iv) Sum of the angles is : . Thus the angles are not supplement to each other.

## ** NCERT ****Solutions for** class 7 maths chapter 5 lines and angles topic 5.2.3

**Solutions for**class 7 maths chapter 5 lines and angles topic 5.2.3

** 1. ** Can two adjacent angles be supplementary?

** Answer: **Yes, two adjacent angles can be supplementary.

For e.g., and 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 and are complementary angles.

** 3. ** Can two obtuse angles be adjacent angles?

** Answer: **Yes, two obtuse angles can be adjacent for e.g., and 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., and 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?

** Answer: **(a) and are adjacent angles as they have common vertex and share a common arm.

(b) and are not adjacent angles as is contained in .

## **NCERT ****Solutions for **class 7 maths chapter 5 lines and angles topic 5.2.4

**Solutions for**class 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 .

But the acute angles have their maximum value of thus their sum cannot be .

** 2. ** Can two obtuse angles form a linear pair?

** Answer: **No two obtuse angles cannot form a linear pair as their sum will exceed , but the sum of angles in linear pair is .

** 3. ** Can two right angles form a linear pair? ** **

** Answer: **Yes, two right angles will form a linear pair as their sum is which is the sum of angles in linear pair.

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

** Answer: **The sum angles of linear pair is .

(i) Sum of the given angles is : . Thus these are linear pair.

(ii) Sum of the given angles is : . Thus these are not linear pair.

(iii) Sum of the given angles is : . Thus these are not a linear pair.

(iv) Sum of the given angles is : . 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 , find and .

** Answer: **From the given figure :

(a) (Vertically opposite angles)

(b) (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

**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.

** 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 :

Also, (Since opposite sides are equal)

Thus

** 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:

** Answer: **The given pair of angles are corresponding angles.

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

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

** (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 pair of angle 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 .

Thus the complementary angle to the given angle is :

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

** Answer: **The sum of the complementary angle is .

Thus the complementary angle to the given angle is :

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

** Answer: **The sum of the complement angles is .

Thus the complement of the angle is given by :

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

**Answer: **We know that sum of supplement angles is

The supplement of the given angle is :

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

**Answer: **We know that the sum of angles of supplementary pair is .

Thus the supplement of the given angle is :

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

** Answer:** We know that the sum of angles of supplementary pair is .

Thus the supplement of the given angle is :

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

**Answer: **We know that the sum of supplementary angles is and the sum of complementary angle is .

(i) Sum of the angles is : . Hence these are supplementary angles.

(ii) Sum of the angles is : . Hence these are complementary angles.

(iii) Sum of the angles is : . Hence these are supplementary angles.

(iv) Sum of the angles is : . Hence these are supplementary angles.

(v) Sum of the angles is : . Hence these are complementary angles.

(vi) Sum of the angles is : . Hence these are complementary angles.

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

** Answer: **Let the required angle be .

Then according to question, we have :

or

or

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

**Answer: **Let the required angle be .

Then according to the question :

or

or

Hence the angle is .

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

** Answer:** Since it is given that and are supplementary angles, i.e. the sum of both angles is .

Thus if is decreased then to maintain the sum 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 .

(i) The maximum value of the sum of two acute angles is less than . Thus two acute angles can never be supplementary.

(ii) The minimum value of the sum of two obtuse angles is more than . Thus two obtuse angles can never be supplementary.

(iii) Sum of two right angles is . Hence two right angles are supplementary.

** 8. ** An angle is greater than . Is its complementary angle greater than or equal to or less than ?

** Answer: **We know that the sum of two complementary angles is .

Thus if one of the angles is greater than then the other angle needs to be less than .

(i) Is adjacent to ?

(ii) Is adjacent to ?

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

(ii) No, is not adjacent to . This is because contains .

(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, and are vertically opposite angles as they are the angles formed by two intersecting straight lines.

(vi) The vertically opposite angle to is _{} .

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

** (i) ** Vertically opposite angles.

** Answer: **The vertically opposite pairs are :

(a) and

(b) and _{}

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

** Answer: **The sum of angles in linear pair is .

Thus the linear pairs are :

(a)

(b)

** 11. ** In the following figure, is adjacent to ? Give reasons.

** Answer: **No, and 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) (Vertically opposite angle)

(ii) (Linear pair)

(iii) (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) (Vertically opposite angle)

(ii) (Linear pair/straight line)

(iii) (Vertically opposite angle).

** (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 _____________.

** Answer: **(i)

(ii)

(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.

** Answer:** (i) are the vertically obtuse angles.

(ii) are the complementary angles.

(iii) are the equal supplementary angles.

(iv) are the unequal pair of supplementary angle.

(v) , and 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?

** 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?

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

** 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 ** **

** Answer: ** (i) Corresponding angles :- , , ,

(ii) Alternate interior angles :- , ,

(iii) Alternate angles on the same side of traversal :- ,

(iv) Vertically opposite angles :- , , ,

** 3. ** In the adjoining figure, . Find the unknown angles.

** Answer: **The angles can be found using different properties:

(a) (The angles are linear pair)

(b) (Vertically opposite angle)

(c) (Corresponding angle)

(d) (Vertically opposite angle)

(e) (Vertically opposite angel, linear pair).

** 4.(i) ** Find the value of in each of the following figures if .

** Answer:** The linear pair of the is :

Thus the value of x is : (Corresponding angles of parallel lines are equal).

** 4.(ii) ** Find the value of in each of the following figures if

** Answer:** The value of x is , as these are the corresponding angles.

** 5. ** In the given figure, the arms of two angles are parallel. If , then find

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

Thus : (Corresponding angles of parallel arms are equal.)

(ii) Further side BC is parallel to EF.

We have : (Corresponding angles of parallel arms are equal.)

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

** Answer**: (i) In this case. the sum of the interior angle is thus l is ** not parallel ** to m.\

(ii) In this case, also l is **not parallel **to m as the corresponding angle cannot be (Linear pair will not form).

(iii) In this l and m are **parallel ** . This is because the corresponding angle is and it forms linear pair with .

(iv) The lines are **not parallel **as the linear pair not form. (Since the corresponding angle will be otherwise.)

### NCERT Solutions for Class 7 Maths Chapter-wise

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Chapter 8 | NCERT solutions for class 7 maths chapter 8 comparing quantities |

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Chapter 15 | NCERT solutions for class 7 maths chapter 15 Visualising Solid Shapes |

### 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.

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

**Question: **Why we study lines and angles

**Answer: **

Lines and angles is the basics of geometry. It will be definitely useful in higher studies. Not only in mathematics but in almost all the subjects.

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