NCERT Solutions For Class 9 Maths Chapter 6 Lines And Angles (Ex 6.1) Exercise 6.1

Class 9 students do their best to ace mathematics examinations. There are a lot of tips that can help make the process a bit easier. One of the most important things is to be sure to understand how to use the theorems and formulas in the particular question that are covered in the textbook. This can be quickly done by reviewing the materials recommended by Extramarks as well as doing any practice problems that are available in the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1. In addition, following the procedures and methods that are used in the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, can be very beneficial for students who want to score high in their exams.

Mathematics is considered the most demanding subject that students learn in school. Mathematics in Class 9 is particularly significant, as it lays the foundation for more advanced Mathematics courses. In Class 9, students learn about basic concepts such as addition, subtraction, multiplication, and division. They also learn about more complex concepts, such as Algebra and Geometry. Students need to do well in Mathematics Class 9, as it will prepare them for future courses. Moreover, Mathematics is a useful skill that can be used in many different fields, for example, Science. Therefore, students need to understand the concepts that are taught in Class 9.

Mathematics is used in the everyday lives of individuals in a variety of ways. They use it to calculate discounts at the store, plan their budgets, and figure out how to get to their destinations on time. Mathematics is used in navigation, with GPS systems relying on Mathematical equations to calculate distances and directions. Even something as simple as cooking can involve Mathematics. Recipes often call for specific measurements, such as teaspoons or cups. Mathematics can be used to make people’s lives easier in several ways. For instance, it can be used to make financial decisions, plan a route for travelling, or figure out how much time it will take to cook something.

Students go through several challenges and problems while solving Mathematical questions. To overcome such challenges students can take help from the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 which is proposed by Extramarks.

NCERT Solutions For Class 9 Maths Chapter 6 Lines and Angles (Ex 6.1) Exercise 6.1 

In the educational system of India, NCERT textbooks are recognised as a comprehensive guidebook for students’ study material. Among all the essential elements of the Indian educational system, the NCERT curriculum is the most important and is treated as a curriculum followed by most students. Its goal is to provide students with a complete understanding of the subjects they are studying in their academic courses. The NCERT curriculum may be profitable to students in various ways. Giving students a firm understanding of the topics it covers is the curriculum’s principal goal. Second, the syllabus is based on CBSE, which is used by educational institutions across the nation (India). The NCERT curriculum results in students being more equipped to do well on the CBSE exams. To incorporate the most recent changes to the syllabus, the NCERT curriculum is frequently modified. Last but not least, the curriculum is delivered in a manner that is approachable and interesting to students, making learning an enjoyable and exciting experience. However, Extramarks provides materials for NCERT Solutions, such as NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, in PDF format for students to download for later usage.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Ex 6.1) Exercise 6.1

NCERT Solutions are a collection of solutions created by Extramarks’ experts to aid students in comprehending the ideas presented in the council-recommended textbooks. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 are created in line with the most recent CBSE syllabus and are accessible for students studying in classes 6 through 12. Both Hindi and English versions are available for them.

The facilities and services offered by Extramarks as described on their website must be understood by students. Extramarks is a pleasant website that provides students with preparation materials, mock exams, and past years’ papers to help students grasp the relevance of using NCERT Solutions, for instance, NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1. An advantage of utilising Extramarks’ first-class services is the opportunity to learn directly from the world’s greatest professors and subject-matter experts. Students may practice the question papers that are available in the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, and also analyse their strengths and weaknesses. Extramarks delivers extensive study materials along with assistance that can be used in the future by students who can download them.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles (Ex 6.1) Exercise 6.1

Students will study Basic terms and definitions of Lines and Angles as well as other vital topics in Chapter 6, Exercise 6.1 of Class 9 in Mathematics subject. The following themes should be well prepared by students while solving Exercise 6.1:

  1. Terms and Definitions – Line Segment, Ray, Collinear and Non-collinear points
  2. Angles – Arms and Vertexes
  3. Types of Angles (7) – Acute Angle, Right Angle, Obtuse Angle, Straight Angle, Reflex Angle, Complementary Angle, and Supplementary Angle
  4. Linear Pair of Angles – Vertically opposite angles
  5. Intersecting Lines and Non-Intersecting Lines
  6. Pair of Angles – Linear (Theorems and Examples)

Exercise 6.1 has 6 questions in total that can be solved with the guidance of NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 emphasised by Extramarks.

Chapter Wise NCERT Solutions For Class 9 Maths

The chapter-wise NCERT Solutions for Class 9 can be found by students on the Extramarks mobile application or website. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, are a great resource for students to understand the concepts of Mathematics and to prepare for exams. These NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, are easy to follow and will help students score better grades. For students’ ease, Extramarks has provided the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 in PDF format, so that, students can download them and refer to them whenever required. Exercise 6.1 Class 9 Solutions, assists students in understanding the questions mentioned in Class 9 Maths Chapter 6 Exercise 6.1. The chapters that are covered in the Class 9 Mathematics subject course are as follows:

  • Chapter 1 – Number Systems
  • Chapter 2 – Polynomials
  • Chapter 3 – Coordinate Geometry
  • Chapter 4 – Linear Equations in Two Variables
  • Chapter 5 – Introduction to Euclid’s Geometry
  • Chapter 6 – Lines and Angles
  • Chapter 7 – Triangles
  • Chapter 8 – Quadrilaterals
  • Chapter 9 – Areas of Parallelograms and Triangles
  • Chapter 10 – Circles
  • Chapter 11 – Constructions
  • Chapter 12 – Heron’s Formula
  • Chapter 13 – Surface Areas and Volumes
  • Chapter 14 – Statistics
  • Chapter 15 – Probability

Students can explore solutions for the above-mentioned Chapters by visiting the Extramarks website. On the other hand, if students are looking for a better understanding of Mathematical concepts in Lines and Angles and want to score well in the exams, they should check out Class 9 Maths Chapter 6 Exercise 6.1 Solution. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 are easy to follow and will help students to understand the concepts sufficiently.

Class 9 Maths Chapter 6 Includes:

In Class 9, Chapter 6 of Mathematics is all about Lines and Angles as the name of the chapter suggests. In this chapter, students will learn how to solve questions regarding Line segments, Types and Pairs of Angles, Intersecting and Non-Intersecting Lines, Parallel Lines and Transversal, Lines Parallel to the same lines, and other topics. These topics have several exercises incorporated into them that students can practice and get a deeper understanding of it. Similarly, if students are not able to solve any particular question, they can take help from the NCERT Solutions, like the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 advised by Extramarks.

NCERT Solutions for Class 9

Class 9 students will find the NCERT Solutions for Exercises questions from the Extramarks website which provides a comprehensive guide for completing their assignments and preparing for examinations. The solutions similar to NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 are well-organized and easy to understand, making them an ideal resource for students. The Exercises in the Class 9 Mathematics NCERT textbook have many questions that need a helping hand for students. The questions are carefully selected to cover all the important concepts. So, students must solve all the exercises carefully. They will have a more in-depth understanding of the ideas and will be able to study well for their examinations as a result. Students should use the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, as a great resource since they offer clear instructions and directions for finishing assignments and getting ready for exams. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, delivered by Extramarks are encouraged by academic scholars and subject-matter professionals.

CBSE Study Materials for Class 9

Class 9 is an important year for students as they prepare for their board exams. The CBSE curriculum is comprehensive and covers a range of topics. To help students achieve success, it is important to have access to good study materials. CBSE provides a lot of study materials for class 9 students. The main materials are textbooks, workbooks, and teacher’s guides. The textbooks are published by NCERT, which is the National Council of Educational Research and Training. Workbooks are designed to help students practice the skills they learn in class, and teachers’ guides include teaching notes, answer keys, and assessment questions.

From mathematics to environmental science, the CBSE study guide for Class 9 covers a wide range of subjects. The curriculum is meant to assist students in getting ready for the board exams, which are a significant turning point in their academic careers. The content is extensive and well organized, making it a crucial tool for both students and their teachers. Further, Extramarks assisted NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, are the best way to acquire good grades in the Mathematics subject.

CBSE Study Materials

CBSE exams are one of the most important exams in India, and it is crucial to be well-prepared for them. One of the finest ways to prepare for the CBSE exam is to use CBSE study materials that are provided by the smartphone application or website of Extramarks. These materials can help students learn the topics and practice for the exams. The best way to use CBSE study materials to help students achieve their best scores is by using them as a guide. The most promising CBSE study materials available online on the Extramarks website are:

  1. The CBSE syllabus, outlines all the topics that will be covered on the exam.
  2. CBSE sample papers, which give students a preview of the types of questions that will be asked on the exam.
  3. CBSE revision notes, which provide a concise summary of all the topics covered in the syllabus.
  4. CBSE past years’ papers, which allow students to practice answering questions under exam conditions.
  5. Extramarks online courses, which provide a more detailed questioning of the syllabus topics.

CBSE study materials can help students prepare for their CBSE exam in the most satisfactory way possible. Students should utilise these materials to achieve their best scores on the CBSE exam. The NCERT Solutions for Exercise 6.1 Class 9 Maths, are simply and quickly accessible to students on Extramarks. These NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 can be downloaded by students so that they can use them when the Mathematics examination approaches.

Q.1 In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠ BOD = 40°, find ∠BOE and reflex ∠COE.


Ans

Given: Lines AB and CE itersect at O and∠AOC+∠BOE=70° and ∠BOD=40°To find: ∠BOE and reflex ∠COE.∠AOB is a straight angle, so              ∠AOB=180°∠AOC+∠COE+∠BOE=180°   70°+∠COE=180°⇒    ∠COE=180°−70°=110°∠COD is a straight angle, so              ∠COD=180°∠COE+∠EOB+∠BOD=180°         110°+∠BOE+40°=180°      ∠BOE=180°−150° =30°          Reflex ∠COE=360°−∠COE           =360°−110°           =250°

Q.2 In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.


Ans

Given:​ Lines XY and MN intersect at O. ∠POY=90° and a:b=2:3To find: cSince, a:b = 2:3 so, let a=2x, b=3x              ∠POX+∠POY=180°                      a+b+90°=180°        2x+3x+90°=180°5x=180°   x=180°5=30°   b=2x       =2×30°       =60°MN is a straight line, so              ∠MOX+∠XON=180°  60°+c=180°      c=180°−60°       =120°

Q.3 In Fig. 6.15, ∠ PQR = ∠ PRQ, then prove that ∠PQS = ∠PRT.


Ans

Given: In ΔPQR,  ∠PQR=∠PRQTo Prove: ∠PQS=∠PRTProof:​ ∠PQR+∠PQS=180°[Linear pair of angles]         ∠PQR=180°−∠PQS   ...(i)                ∠PRQ+∠PRT=180°[Linear pair of angles]          ∠PRQ=180°−∠PRT   ...(ii)But    ∠PQR=∠PRQ[Given]⇒180°−∠PQS=180°−∠PRT⇒    ∠PQS=∠PRTHence Proved.

Q.4 In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.


Ans

Given: x+y=w+zTo Prove: AOB is a line.Proof:   ∵x+y+w+z=360°             [Complete​​ angle]x+y+x+y=360°            [∵x+y=w+z]        2(x+y)=360°     x+y=360°2      =180°   ∠AOB =180°⇒Since,∠AOB is a straight angle, so AOB is a straight line.

Q.5 In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ.
OS is another ray lying between rays OP and OR. Prove that ∠ROS = (1/2)(∠QOS – ∠POS).


Ans

Given:​ POQ is a line. OR→⊥PQ and OS→ is another ray between       OR→​ and OP→.To Prove: ∠ROS = 12(∠QOS−∠POS)Proof:R.H.S.= 12(∠QOS−∠POS)         =12{(∠QOR+∠ROS)−(∠ROP−∠ROS)}         =12{(90°+∠ROS)−(90°−∠ROS)}      [∠QOR=∠ROP          =90°]        =12(∠ROS+∠ROS)        =12(2∠ROS)         =∠ROS

Q.6 It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information.
If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.


Ans

Given: ∠XYZ=64°, XY is produced to point P.Ray YQ bisects ∠ZYP.To find: ∠XYQ and reflex ∠QYP.​ Since, YQ→ bisects∠ZYP, so ∠ZYQ=∠PYQ=a(let) ∠XYZ+∠ZYP=180° [Linear pair of angles.]            64°+2a=180°   2a=180°−64° =116°      a=116°2 =58°∴       ∠XYQ=64°+a =64°+58° =122°            reflex ∠QYP=360°−∠QYP =360°−58° =302°

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FAQs (Frequently Asked Questions)

Numerous students find it problematic to study Hindi solutions, while a similar number find studying English solutions difficult. However, Extramarks makes it simple for students having such dilemma, as it provides the NCERT Solutions in both the Hindi and the English versions. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 in Hindi are often more extensive and go into greater depth of knowledge about the topics stated in the chapter than the English versions. This is one of the primary variations between the two languages in NCERT Solutions. Contrary to that, the English NCERT Solutions tend to be shorter and simpler to read. If students are seeking a summary of the subject, English solutions can be an excellent choice. Therefore, both of the versions that are offered on the Extramarks website and mobile application must be tested out by students. An example of such a study guide can be NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1, which are available on the Extramarks website.

The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 would be pretty helpful for those students who want to enhance their Mathematical and analytical skills. Students would be better able to understand the concepts covered in the textbook with the support of the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 advised by Extramarks. Students may prepare for examinations by using the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 compiled by Extramarks. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 may be really helpful to excellently apprehend the concept of Lines and Angles. Additionally, the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 could help students improve their ability to solve Mathematics related queries. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 should thus be fully utilised by students to be able to give an outstanding performance in their examination. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 can help students gather ideas and knowledge about the topics included in the syllabus and prepare for their Mathematics exam. The NCERT Solutions like, NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 can be of tremendous help when it comes to apprehending any subject. As a result, if students want to ace their exams, they just need to go through the NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1. The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 are updated annually on Extramarks, in case there are any changes in the CBSE study materials.