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

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NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1 - FREE PDF Download

NCERT Solutions for Class 7 Maths Chapter 5 - Lines and Angles Exercise 5.1, provided by Vedantu. This exercise covers the fundamental concepts of lines and angles, which are essential for understanding basic geometry. The focus is on different types of lines like parallel and perpendicular lines, and various types of angles including acute, obtuse, and right angles.

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Table of Content
1. NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1 - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 5 Exercise 5.1 Class 7 | Vedantu
3. Access NCERT Solutions Class 7 Maths NCERT Chapter 5 Lines and Angles Exercise 5.1
4. Class 7 Maths Chapter 5: Exercises Breakdown
5. CBSE Class 7 Maths Chapter 5 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 7 Maths
FAQs


In Class 7 Maths 5.1, it is important to understand the definitions and properties of lines and angles. Pay close attention to how angles are formed and measured, as these basics are crucial for solving more complex geometric problems. Vedantu's detailed solutions will help you master these concepts and strengthen your mathematical foundation.


Glance on NCERT Solutions Maths Chapter 5 Exercise 5.1 Class 7 | Vedantu

  • NCERT Solutions Maths Exercise 5.1 Class 7 includes Introduction to Lines and Angles, Complementary Angles, and Supplementary Angles.

  • When the sum of the measures of two angles is 90°, the angles are called complementary angles.

  • Whenever two angles are complementary, each angle is said to be the complement of the other angle.

  • Supplementary angles are two angles that add up to 180 degrees.

  • There are ten questions in class 7 maths ex 5.1 which are fully solved by experts at Vedantu.

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

Refer to page 3-6 for Exercise 5.1 in the PDF.

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

(i)

Angle 20 degrees

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $20^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then,

$ = x + 20^\circ  = 90^\circ $

$ = x = 90^\circ  - 20^\circ $

$ = x = 70^\circ $

Hence, the complement of the given angle measures $70^\circ $.

(ii) 

Angle 63 degrees

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $63^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then,

$ = x + 63^\circ  = 90^\circ $

$ = x = 90^\circ  - 63^\circ $

$ = x = 27^\circ $

Hence, the complement of the given angle measures $27^\circ $.

(iii)

Angle 57 degrees

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $57^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then, 

$ = x + 57^\circ  = 90^\circ $

$ = x = 90^\circ  - 57^\circ $

$ = x = 33^\circ $

Hence, the complement of the given angle measures $33^\circ $.

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

i) 

Angle 105 degrees

Ans: Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $105^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 105^\circ  = 180^\circ $

$ = x = 180^\circ  - 105^\circ $

$ = x = 75^\circ $

Hence, the  supplement of the given angle measures $75^\circ $

ii) 

Angle 87 degrees

Ans: Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $87^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 87^\circ  = 180^\circ $

$ = x = 180^\circ  - 87^\circ $

$ = x = 93^\circ $

Hence, the  supplement of the given angle measures $93^\circ $

iii) 

Angle 154 degrees

Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $154^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 154^\circ  = 180^\circ $

$ = x = 180^\circ  - 154^\circ $

$ = x = 26^\circ $

Hence, the  supplement of the given angle measures $26^\circ $


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

i) $65^\circ ,115^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 65^\circ  + 115^\circ $

$ = 180^\circ $

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

Therefore, these angles are supplementary angles.

ii) $63^\circ ,27^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 63^\circ  + 27^\circ $

$ = 90^\circ $

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

Therefore, these angles are complementary angles.

iii) $112^\circ ,68^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 112^\circ  + 68^\circ $

$ = 180^\circ $

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

Therefore, these angles are supplementary angles.

iv) $130^\circ ,50^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 130^\circ  + 50^\circ $

$ = 180^\circ $

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

Therefore, these angles are supplementary angles.

v) $45^\circ ,45^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 45^\circ  + 45^\circ $

$ = 90^\circ $

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

Therefore, these angles are complementary angles.

vi) $80^\circ ,10^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 80^\circ  + 10^\circ $

$ = 90^\circ $

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

Therefore, these angles are complementary angles.

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

Ans: Firstly, let the measure of the required angle be $x^\circ $

As we know that, the sum of measures of complementary angle Pair is $90^\circ $.

Then,

$ = x + x = 90^\circ $

$ = 2x = 90^\circ $

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

$ = x = 45^\circ $

Hence, the required angle measure is $45^\circ $.

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

Ans: Firstly, let the measure of the required angle be $x^\circ $

As we know that, the sum of measures of supplementary angle Pair is $180^\circ $.

Then,

$ = x + x = 180^\circ $

$ = 2x = 180^\circ $

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

$ = x = 90^\circ $

Hence, the required angle measures 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 angles still remain supplementary.

Figure with two supplementary angles

Ans: In the question, it is given that,

$\angle 1$and$\angle 2$are both supplementary angles.

If $\angle 1$is decreased, then $\angle 2$ must be increased by the same value. Hence, this angle pair remains supplementary.

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

i) Acute?

Ans: No. If two angles are acute, it means less than $90^\circ $, the two angles cannot be supplementary.  Because, their sum will be always less than $90^\circ $.

ii) Obtuse?

Ans: No. If two angles are obtuse, it means more than $90^\circ $, the two angles cannot be supplementary.  Because, their sum will always be more than $90^\circ $.

iii) Right?

Ans: Yes. If two angles are right, it means both measures$90^\circ $, the two angles can form a supplementary pair.  Because, their sum will be equal to$90^\circ $.

$\therefore 90^\circ  + 90^\circ  = 180^\circ $.

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

Ans: Here, let us assume that the complementary angles be p and q.

As we know, the sum of measures of complementary angle pairs is $90^\circ $.

Then,

$ = p + q = 90^\circ $

It is given in the question that angle $p > 45^\circ $.

Now, adding q on both the sides, 

$ = p + q > 45^\circ  + q$

$ = 90^\circ  > 45^\circ  + q$

$ = 90^\circ  - 45^\circ  > q$

$ = q < 45^\circ $

Hence, its complementary angle is 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) If two adjacent angles are supplementary, they form a ______.

Ans: Linear pair

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

Adjoining figure with pair of angles

i) Obtuse vertically opposite angles

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


ii) Adjacent complementary angles

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

iii) Equal supplementary

Ans: $\angle EOB$ and $\angle EOD$ are equal supplementary angles in the given figure.

iv) Unequal supplementary angles

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

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

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


Conclusion

Class 7 Maths Ex 5.1 is vital for building a strong foundation in geometry. It focuses on the fundamental properties of lines and angles, including parallel and perpendicular lines, and acute, obtuse, and right angles. Understanding these basics is essential for solving more complex problems in future chapters. Pay close attention to the definitions and properties, as they are crucial for grasping the concepts. Vedantu’s detailed solutions will guide you through these topics, ensuring you develop a solid understanding and excel in your studies.


Class 7 Maths Chapter 5: Exercises Breakdown

Exercises

Number of Questions

Exercise 5.2

6 Questions & Solutions



CBSE Class 7 Maths Chapter 5 Other Study Materials



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.




Important Related Links for NCERT Class 7 Maths

Access these essential links for NCERT Class 7 Maths, offering comprehensive solutions, study guides, and additional resources to help students master language concepts and excel in their exams.


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

1. Is chapter 5 Lines and Angles in NCERT Class 7 Maths important?

Absolutely yes Chapter 5 Lines and Angles is a very important chapter in Class 7 Maths. This will give you a base for the upcoming classes and also be useful for any competitive exams. So, students should give this chapter extra focus and understand the concepts. You can refer to Vedantu, where you can get detailed and stepwise solutions to Chapter 5 Lines and Angles in the free PDF format. Also, you will be able to build a better understanding level and learn a different approach to solving the problem of lines and angles.

2. How many questions are there in NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1?

There are a total of 13 questions in Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 Solutions to all these questions are being provided by Vedantu, and these are available on the official website of Vedantu and the mobile application of Vedantu. The best part is that these NCERT solutions were specially designed by qualified teacher experts, and they are available to students free of charge.

3. How beneficial are NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 for board exams?

NCERT Solutions for Class 7 Maths, Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 provides answers with detailed descriptions as per the syllabus prescribed by the CBSE board. For the students to finish the assignment on time, solving these solutions would be fantastic practice. The NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 are obviously necessary to achieve excellent exam scores. Students can practice writing exams and become more comfortable with the process

4. Mention What Important Topics are Covered in NCERT Solutions Class 7 Math Chapter 5 Lines and Angles?

The most crucial concepts covered in NCERT Solutions Class 7 Maths Chapter 5  Lines and angles are relative angles and their properties, complementary and supplementary angles, adjacent angles, linear pairs, vertically opposite angles, pairs of lines, intersecting lines, transversals, the angle made by a transversal, a transversal of parallel lines, and checking for parallel lines. These subjects are thoroughly covered, along with each topic's unique qualities, which are used to answer many of the chapter's puzzles.

5. How can NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 be helpful in the final exams?

Chapter 5 of Class 7 Math's "Lines and Angles" covers topics like "Complementary Angles," "Supplementary Angles," "Linear Pair," etc. Students may have trouble with fundamental issues when working through these NCERT practice solutions. Vedantu offers free NCERT solutions that use a simple methodology so that students can grasp the fundamentals while answering these questions. In addition, they will be ready for challenging questions before their final exams.

6. Can I download the NCERT Solutions for class 7th exercise 5.1 for free?

Yes, you can download the NCERT Solutions for class 7 exercise 5.1 for free. These solutions are available on various educational websites, including the official NCERT website. They are designed to help students understand and solve the problems in the exercise. Accessing these solutions can provide additional support and clarification for students. Moreover, the free availability ensures that all students can benefit from these resources.

7. Are these exercise 5.1 class 7 solutions useful for competitive exams?

Yes, the solutions for Exercise 5.1 are useful for competitive exams. They cover fundamental concepts and problem-solving techniques that are frequently tested in various school-level competitive exams. By practising these solutions, students can strengthen their understanding and improve their problem-solving skills. These solutions also help in building a strong foundation in geometry, which is beneficial for higher-level exams. Therefore, regular practice with these solutions can aid in overall exam preparation.

8. Can these solutions help me prepare for exams?

Yes, NCERT solutions of class 7 ex 5.1 are excellent for exam preparation. They provide detailed explanations and step-by-step solutions, which help in understanding the concepts and practising problem-solving techniques.

9. How should I use these solutions to improve my understanding in class 7 maths exercise 5.1?

To improve your understanding in class 7 maths exercise 5.1, start by attempting the problems on your own. After solving, use the solutions to check your answers and identify any mistakes. Carefully review the step-by-step explanations provided in the solutions. This will help you understand the correct approach and methodology for solving the problems.