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NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Last updated date: 07th Aug 2024
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NCERT Solutions for Class 7 Maths Lines and Angles Chapter 5 - FREE PDF Download

NCERT for Chapter Lines and Angles class 7 form the foundation of geometry, making it essential for students to grasp these concepts thoroughly. Chapter 5 of Class 7 Maths delves into the basics of lines, different types of angles, and their properties. Understanding these concepts will help you solve various geometrical problems and prepare you for more advanced topics in higher classes.

Table of Content
1. NCERT Solutions for Class 7 Maths Lines and Angles Chapter 5 - FREE PDF Download
2. Glance on Maths Chapter 5 Class 7 - Lines and Angles
3. Access Exercise wise NCERT Solutions for Chapter 5 Maths Class 7
4. Exercises Under NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles
5. Access NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles
5.1Exercise 5.1
5.2Exercise  5.2
6. Overview of Deleted Syllabus for CBSE Class 7 Maths Lines and Angles
7. Class 7 Maths Chapter 5: Exercises Breakdown
8. Other Study Material for CBSE Class 7 Maths Chapter 5
9. Chapter-Specific NCERT Solutions for Class 7 Maths
FAQs

In class 7 maths Ch 5, we focus on the types of angles such as acute, obtuse, and right angles, as well as complementary and supplementary angles. Pay special attention to the properties of intersecting and parallel lines, as these are crucial for solving problems. NCERT Solutions for Class 7 Maths Lines and Angles Chapter 5 provides a strong base to tackle exercises confidently and accurately.

Glance on Maths Chapter 5 Class 7 - Lines and Angles

• Lines are understood as the concept of infinitely long, straight paths with no beginning or end.

• Differentiating Rays and Line Segments: Rays (one endpoint) and line segments (two endpoints) - both parts of a line.

• Angles: Discovering how lines or line segments intersect to form angles.

• Measuring Angles: Learning to use protractors to measure angles in degrees.

• Classifying Angles: Categorizing angles based on their size:

• Acute (< 90°)

• Right (90°)

• Obtuse (> 90° and < 180°)

• Straight (180°)

• Reflex (> 180°)

• There are two exercises (16 fully solved questions) in Class 7th Maths Chapter 5 Lines And Angles.

Access Exercise wise NCERT Solutions for Chapter 5 Maths Class 7

 Current Syllabus Exercises of Class 7 Maths Chapter 5 NCERT Solutions of Class 10 Maths Lines and Angles Exercise 5.1 NCERT Solutions of Class 10 Maths Lines and Angles Exercise 5.2

Exercises Under NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Exercise 5.1: Pairs of Angles

• Complementary and Supplementary Angles: Problems where students determine if angles are complementary or supplementary and calculate the unknown angles.

• Adjacent and Vertically Opposite Angles: Exercises focusing on identifying and calculating adjacent and vertically opposite angles in given diagrams.

Exercise 5.2: Transversal and Angles Formed

• Angles Formed by a Transversal: Questions about identifying corresponding, alternate interior, and alternate exterior angles when a transversal cuts through parallel lines.

• Calculations and Proofs: Problems involving calculating unknown angles and proving certain angle properties using theorems.

Access NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles

Exercise 5.1

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

Ans: For finding complement angle we use = $90{}^\circ -$ given angle

1. Complement of $20{}^\circ = 90{}^\circ -20{}^\circ =70{}^\circ$

2. Complement of $63{}^\circ =90{}^\circ -63{}^\circ =27{}^\circ$

3. Complement of $57{}^\circ =90{}^\circ -57{}^\circ =33{}^\circ$

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

Ans: For finding supplement angle we use = $180{}^\circ -$ given angle

1. Supplement of $105{}^\circ = 180{}^\circ -105{}^\circ =75{}^\circ$

2. Supplement of $87{}^\circ =180{}^\circ -87{}^\circ =93{}^\circ$

3. Supplement of $154{}^\circ =180{}^\circ -154{}^\circ =26{}^\circ$

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

 $65{}^\circ ,115{}^\circ$ $63{}^\circ ,27{}^\circ$ $112{}^\circ ,68{}^\circ$ $130{}^\circ ,50{}^\circ$ $45{}^\circ ,45{}^\circ$ $80{}^\circ ,10{}^\circ$

Ans: If the sum of two angles is $180{}^\circ$, then they are called supplementary angles.

If the sum of two angles is $90{}^\circ ,$ then they are called complementary angles.

1. $65{}^\circ +115{}^\circ =180{}^\circ$

The sum of two angles is $180{}^\circ$. Thus, these are supplementary angles

1. $63{}^\circ +27{}^\circ =90{}^\circ$

The sum of two angles is $90{}^\circ$. Thus, these are complementary angles

(iii) $112{}^\circ +68{}^\circ =180{}^\circ$

The sum of two angles is $180{}^\circ$. Thus, these are supplementary angles

(iv) $130{}^\circ +50{}^\circ =180{}^\circ$

The sum of two angles is $180{}^\circ$. Thus, these are supplementary angles

(v) $45{}^\circ +45{}^\circ =90{}^\circ$

The sum of two angles is $90{}^\circ$. Thus, these are complementary angles

(vi) $80{}^\circ +10{}^\circ =90{}^\circ$

The sum of two angles is $90{}^\circ$. Thus, these are complementary angles

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

Ans: Let one of the two complementary angles be $x$

$\therefore x+x=90{}^\circ$

$2x=90{}^\circ$

$x=\frac{90}{2}$

$x=45{}^\circ$

Thus, $45{}^\circ$is the angle equal to its complement.

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

Ans: Let one of the two supplementary angles be $x$

$\therefore x+x=180{}^\circ$

$2x=180{}^\circ$

$x=\frac{180}{2}$

$x=90{}^\circ$

Thus, $90{}^\circ$is the angle equal to its complement.

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

Ans: If $\angle 1$is decreased then, $\angle 2$will be increasing with the

same measure in the way that both the angles still remain supplementary.

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

(i). acute

Ans: No, because sum of two acute angles is less than $180{}^\circ$

(ii). Obtuse

Ans: No, because sum of two obtuse angles is more than $180{}^\circ$

(iii). right?

Ans: Yes, because sum of two right angles is equal to $180{}^\circ$

8. An angle is greater than $45{}^\circ$. Is its complementary angle greater than $45{}^\circ$ or equal to $45{}^\circ$ or less than $45{}^\circ$ ?

Ans: Let the complementary angles be $x$and$y$, i.e., $x+y=90{}^\circ$

Given, $x>45{}^\circ$…………….$\left( i \right)$

Adding $y$to both sides in eq. $\left( i \right)$

$x+y>45{}^\circ +y$

$90{}^\circ >45{}^\circ +y$

$90{}^\circ -45>y$

$45{}^\circ >y$

Thus, the complementary angle will be less than $45{}^\circ$

9. Fill in the blanks:

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

Ans: $90{}^\circ$

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

Ans: $180{}^\circ$

(iii). Two angles forming a linear pair are _______________.

Ans: Supplementary

(iv). If two adjacent angles are supplementary, they form a _______________.

Ans: Linear Pair

(v). If two lines intersect a point, then the vertically opposite angles are always

_______________.

Ans: 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 _______________.

Ans: Obtuse Angles

10. In the adjoining figure, name the following pairs of angles:

(i). Obtuse vertically opposite angles.

Ans: In the given figure, $\angle AOD$and$\angle BOC$ are obtuse vertically opposite angles.

Ans: In the given figure, $\angle AOB$ and $\angle EOA$ are adjacent complementary angles.

(iii). Equal supplementary angles.

Ans: In the given figure, $\angle EOB$ and $\angle EOD$ are equal supplementary angles

(iv). Unequal supplementary angles.

Ans: In the given figure, $\angle EOA$ and$\angle EOC$ are unequal supplementary angles.

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

Ans: In the given figure, $\angle AOB$ and $\angle EOA$, $\angle EOA$ and $\angle EOD$, $\angle EOD$ and $\angle COD$ are adjacent angles that do not form a linear pair.

Exercise  5.2

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

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

Ans: Given, $\angle 1$

than $\angle 1$ = $\angle 5$, (Corresponding Angle)

If the two parallel ($a$$\parallel$$b$) lines cut by a transversal ($b.$),

then each pair of corresponding angles will be equal in measure.

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

Ans: Given, $\angle 4=\angle 6$ (Alternate Interior Angles)

than, $a$$\parallel$$b$

When a transversal ($b.$) cut two lines such that pairs of alternate interior angles are equal, then the lines will be parallel $a$$\parallel$$b$.

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

Ans: Given, $\angle 4+\angle 5=180{}^\circ$,

Then $a$$\parallel$$b$

When a transversal ($b.$) cut two lines such that pairs of interior angles on the same side of transversal are supplementary ($\angle 4+\angle 5=180{}^\circ$), the lines have to be parallel ($a$$\parallel$$b$).

2. In the adjoining figure, identify:

(i). the pairs of corresponding angles.

Ans: The pair of corresponding angles are:

($\angle 1,\angle 5$), ($\angle 2,\angle 6$), ($\angle 4,\angle 8$) & ($\angle 3,\angle 7$)

(ii). the pairs of alternate interior angles.

Ans: The pair of alternate interior angles are:

($\angle 3,\angle 5$) & ($\angle 2,\angle 8$)

(iii). the pairs of interior angles on the same side of the transversal.

Ans: The pair of interior angles on the same side of the transversal are:

($\angle 3,\angle 8$) & ($\angle 2,\angle 5$)

(iv). the vertically opposite angles.

Ans: The vertically opposite angles are:

($\angle 1,\angle 3$), ($\angle 2,\angle 4$), ($\angle 6,\angle 8$) & ($\angle 5,\angle 7$)

3. In the adjoining figure, $p$$\parallel $$q. Find the unknown angles. Ans: Given, $p$\parallel$$q$ and is cut by a transversal line

$\therefore$ $125{}^\circ +\angle e=180{}^\circ$ (Linear Pair)

$\Rightarrow \angle e=180{}^\circ -125{}^\circ$

$\Rightarrow \angle e=55{}^\circ$

Now, $\angle e=\angle f=55{}^\circ$ (Vertically Opposite Angles)

So, $\angle f=\angle a=55{}^\circ$ (Alternate Interior Angles)

$\Rightarrow \angle a+\angle b=180{}^\circ$ (Linear Pair)

$\Rightarrow 55{}^\circ +\angle b=180{}^\circ   \Rightarrow \angle b=180{}^\circ -55{}^\circ   \Rightarrow \angle b=125{}^\circ$

Now, $\angle a=\angle c=55{}^\circ   \angle b=\angle d=125{}^\circ$ (Vertically Opposite Angles)

Hence, $\angle a=55{}^\circ ,\angle b=125{}^\circ ,\angle c=55{}^\circ ,\angle d=125{}^\circ ,\angle e=55{}^\circ \And \angle f=55{}^\circ$

4. Find the values of x in each of the following figures if $l\parallel m$.

Ans: $(i)$ Given, $l\parallel m$and t is transversal line.

$\therefore$ Interior vertically opposite angle between lines $l$and$t$

$\therefore$ $110{}^\circ +x=180{}^\circ$ (Supplementary Angles)

$x=180{}^\circ -110{}^\circ$

$x=70{}^\circ$

$(ii)$ Given, $l\parallel m$and t is transversal line.

$x+2x=180{}^\circ$ (Interior Opposite Angles)

$3x=180{}^\circ$

$x=\frac{180{}^\circ }{3}$

$x=60{}^\circ$

$(iii)$ Given, $l\parallel m$ and $a\parallel b$

$x=100{}^\circ$ (Corresponding Angles)

5. In the given figure, the arms of two angles are parallel. If ∆ABC = $70{}^\circ$, then find:

(i). ∠ DGC (ii) ∠ DEF

Ans:

$(i)$ Given, $AB$$\parallel$$DE$ and BC is a transversal line and $\angle$ABC$=70{}^\circ$

$\therefore$ $\angle$ABC$=$$\angle$DGC$=70{}^\circ$ (Corresponding Angles)

$\angle$DGC$=70{}^\circ$

$(ii)$ Given, $BC$$\parallel$$DF$ and DE is a transversal line and $\angle$DGC$=70{}^\circ$

$\angle$DGC$=$$\angle$DEF$=70{}^\circ$ (Corresponding Angles)

$\angle$DEF$=70{}^\circ$

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

Ans: $(i)$ $126{}^\circ +44{}^\circ =170{}^\circ$

l is not parallel to m because sum of interior opposite angles should

be $180{}^\circ$

$(ii)$ $75{}^\circ +75{}^\circ =150{}^\circ$

l is not parallel to m because sum of angles is not obeying parallel

lines rules.

$(iii)$$57{}^\circ +123{}^\circ =180{}^\circ$

l is parallel to m because sum of supplementary angles is $180{}^\circ$

$(iv)$$98{}^\circ +72{}^\circ =170{}^\circ$

l is not parallel to m because sum of angles is not obeying parallel

lines rules.

Overview of Deleted Syllabus for CBSE Class 7 Maths Lines and Angles

 Chapter Dropped Topics Lines and Angles 5.2.3 Adjacent angles 5.2.4 Linear pairs 5.2.5 Vertically opposite angles

Class 7 Maths Chapter 5: Exercises Breakdown

 Exercise Number of Questions Exercise 5.1 10 Questions & Solutions Exercise 5.2 6 Questions & Solutions

Conclusion

NCERT Maths class 7 chapter 5 - Lines and Angles is crucial for building a solid understanding of geometry. Focus on learning the different types of angles and pairs of angles, along with the properties of parallel lines. Key concepts include acute, obtuse, and right angles, as well as complementary and supplementary angles. Last year's exam featured around 3–4 questions from this chapter, highlighting both theory and practical problems. Regular practice with NCERT Solutions will ensure you grasp these concepts well. Keep studying and clarifying your doubts to excel in geometry!

Chapter-Specific NCERT Solutions for Class 7 Maths

Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

FAQs on NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

1. What are the main contents of Class 7 Maths Chapter 5 Lines and Angles?

The main topics that are included in the fifth chapter of Class 7 Maths Lines and Angles are:

1. Introduction

2. Related Angles

1. Complementary Angles

2. Supplementary Angles

4. Linear Pair

5. Vertically Opposite Angles

3. Pairs of Lines

1. Intersecting Lines

2. Transversal

3. Angles made by a Transversal

4. Transversal of Parallel Lines

4. Checking for Parallel Lines

Students can find the solutions to the NCERT textbook questions related to these topics on Vedantu’s site. This will help students to clear all their doubts regarding the chapter.

2. How are NCERT Solutions for Class 7 Maths Chapter 5 useful for students?

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles is the best study material for practising and revising the chapter. Especially for those students who are finding difficulties in solving problems, these solutions by the expert teachers are immensely helpful. NCERT Solutions for Class 7 Maths Chapter 5  is really helpful to understand the chapter and clear the doubts quickly. Students can score well in the exam by referring to NCERT Solutions for Class 7 Maths available in the free PDF format.

3. Where can I find good quality NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles?

There are many online platforms available that cater to chapter-wise NCERT Solution for Class 7 Mathematics. However, it is crucial to download the same from the authentic site which offers the complete coverage of the exercise questions. Vedantu is one such site where one can find good quality NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles. These solutions include stepwise explanations of the exercise problems. Also, these are available for free download, in high-resolution PDF quality. Hence, students need not struggle in finding the solutions. They can instantly clear their doubts regarding the chapter with the help of Vedantu’s NCERT Solutions for Class 7 Maths Chapter 5.

4. What are the key features of Vedantu’s NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles?

Following are some of the key features of NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles provided by Vedantu:

• Easy to Access: NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles are available in the free to download PDF form.

• Created by Expert Tutors: These solutions are created by experts. Hence, these are 100% verified.

• Complete Syllabus Coverage: NCERT Solutions for Class 7 Maths for chapter 5 as well as ad other chapters provide complete coverage of the exercise questions.

• As per the Board Guidelines: These solutions are prepared at Vedantu as per the CBSE board guidance and the latest exam pattern.

5. What are the Important Topics Covered in NCERT Solutions Class 7 Maths Chapter 5?

The most important topics covered in NCERT Solutions Class 7 Maths Chapter 5 are Relative Angles And Their Properties, Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pairs, Vertically Opposite Angles, Pair Of Lines, Intersecting Lines, Transversal, The Angle Made By A Transversal, A Transversal Of Parallel Lines And Checking For Parallel Lines. These topics are explained thoroughly with their respective properties in great detail that are used to solve various questions in this chapter.

6. How Many Questions are there in NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles?

There are two exercises in NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles. Exercise 5.1 has 14 questions with most of its questions having multiple subparts. Exercise 5.2 has six questions with its questions having sub-parts as well. These questions revolve around the basic topics of the chapter Lines and Angles and to solve them, one requires the knowledge of all the concepts that are given in the chapter. To check the solutions, students can download the NCERT Solutions free of cost from Vedantu platform.

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

Relative Angles And Their Properties, Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pairs, Vertically Opposite Angles, Pair Of Lines, Intersecting Lines, Transversal, The Angle Made By A Transversal, A Transversal Of Parallel Lines, And Checking For Parallel Lines are some of the important topics covered in NCERT Solutions Class 7 Maths Chapter 5. All the solutions to these topics are easily available on Vedantu website and the app.

8. How is NCERT Solution for Class 7 Maths Chapter 5 helpful for board exams?

The NCERT Solution for Class 7 Maths Chapter 5 is very helpful for board exams as all the questions are answered with utmost precision with all the formulae written along to make it convenient for the students to revise along. These questions set the base for board examination as they are very concept based questions and hence have to be answered tactfully. The NCERT Solutions will not only help the students understand the answers better, but they will also help them remember the key concepts.

9. How to score full marks in Class 7 Maths Chapter 5?

To score full marks in any domain of Maths, you must do only one thing - practice. Practice is not only the key to understanding all the concepts on a deeper level, but it will also help you avoid silly mistakes. You will also get to know the kind of answer the question demands and will be able to frame your answers better.

10. What are complementary angles in lines and angles class 7 solutions?

In lines and angles class 7 solutions complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, the other must measure 60 degrees to be complementary. This concept is crucial in understanding various geometric shapes and solving problems involving right angles.

11. How do you identify parallel lines in lines and angles class 7?

In lines and angles class 7 Parallel lines are lines in a plane that do not intersect, no matter how far they are extended. They are always the same distance apart. A common way to identify parallel lines is by looking for the same slope or by using corresponding angles formed by a transversal line.

12. What is the significance of the transversal in geometry in lines and angles class 7 ?

In lines and angles class 7, a transversal is a line that intersects two or more other lines at different points. It plays a significant role in geometry as it helps in identifying angle relationships, such as corresponding angles, alternate interior angles, and alternate exterior angles, which are key in solving various geometric problems.