Prove that AB CD. ∵ PQ || RS ⇒ BL || CM Exercise 4A. ∴ ∠XYZ + ∠ZYQ + ∠QYP = 180° In Fig. From (1) and (2), x = y Again, AB || CD From the diagram, b+c also forms a straight angle so. ∴ 40° + ∠BOE = 70° or ∠BOE = 70° -40° = 30° UP board high school students also use these solutions as UP Board Solutions updated for academic session 2020-2021. ⇒ ∠XYQ = 64° + 58° = 122° [∠QYP = 58°] and EF || ST [Construction] When you have to find the height of a tower or location of an aircraft, then you need to know angles. [Angle sum property of a triangle] {Angle sum property of a triangle] ∠PRS = ∠P + ∠PQR [Alternate interior angles] These expert faculty solve and provide the NCERT Solution for Class 9, which would help students to solve the problems comfortably. These solutions help students prepare for their upcoming Board Exams by covering the whole syllabus, in accordance with the NCERT guidelines. By putting the value of XYZ = 64° and ZYQ = 58° we get. MCQ Questions for Class 9 Maths Chapter 6 Lines and Angles with Answers MCQs from Class 9 Maths Chapter 6 – Lines and Angles are provided here to help students prepare for their upcoming Maths exam. Basic terms and definitions related to a line segment, ray, collinear points, non-collinear points, intersecting and non-intersecting lines. RD Sharma Solutions for Class 9 Mathematics CBSE, 10 Lines and Angles. x = 126°. [Angle sum property of a triangle] In Fig. Question 1. In the figure, we have CD and PQ intersect at F. [Vertically opposite angles] OS is another ray lying between rays OP and OR. Thus, these are some questions for the different chapters starting from Class 9 Chapter 8 Introduction to Lines and Angles. Again, AB || CD and PR is a transversal. ∴ ∠COA = 40° [Linear pair] ∴ x + y + ⇒ + w = 360° or, (x + y) + (⇒ + w) = 360° i. e., a pair of alternate interior angles are equal. ∴ Its complement = 90° – x. To access interactive Maths and Science Videos download BYJU’S App and subscribe to YouTube Channel. Again, PQ ⊥ PS ⇒ AP = 90° ⇒ ∠ABL = ∠MCD …(2) [By (1)] Viz. 6.16, if x+y = w+z, then prove that AOB is a line. We, in our aim to help students, have devised detailed chapter wise solutions for them to understand the concepts easily. Thus, ∠AGE = 126°, ∠GEF=36° and ∠FGE = 54°. ∴ b + a = 180° – 90° = 90° …(i) 6.13, lines AB and CD intersect at O. ⇒ z + y = 180° … (2) [By (1)] Karnataka Board Class 9 Maths Chapter 3 Lines and Angles Ex 3.1. ∴ AB || EF [Exterior angle property of a triangle] In ∆PRT, we have ∠P + ∠R + ∠PTR = 180° Thus, SPR (SPR = 135°) is equal to the sum of interior opposite angles. ⇒ ∠YOZ = 180° -27° – 32° = 121° Adding (1) and (2), we have 5. Q 1. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE. As they are pair of alternate interior angles. We followed the latest Syllabus, while creating the NCERT Solutions and it is framed in accordance with the exam pattern of the CBSE Board. In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. ⇒ 90° + 37° + y = 180° 1. Ex 6.2 Class 9 Maths Question 6. Thus, ∠SQT = 60°, Ex 6.3 Class 9 Maths Question 5. But ∠GED = 126° [Given] Ex 6.1 Class 9 Maths Question 3. ⇒ y = 127°- 50° = 77° Answer : Q2 : In the given figure, lines XY and MN intersect at O. AB || DE and AE is a transversal. These solutions are designed by subject matter experts who have assembled model questions covering all the exercise questions from the textbook. or ∠FGE = 180° – 126° = 54° If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠ BOE and reflex ∠ COE. Now, by putting the values of AOC+BOE = 70° and BOD = 40° we get. Now, you must be wondering why we are studying Lines and Angles. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions. ⇒ ∠QRS = 110° – 50° = 60° AB || CD and GE is a transversal. ∴ ∠AED = 35° ∴∠QRF = ∠QRS + ∠SRF = 110° …(1) We know that a linear pair is equal to 180°. 5. NCERT Solutions for Class 9th: Ch 6 Lines and Angles Maths. While practising the model solutions from this chapter, you will also learn to use the angle sum property of a triangle while solving problems. Solution: (i) Angle – When two rays originate from the same end point, then an angle is formed. [YQ bisects ∠ZYP so, ∠QYP = ∠ZYQ] ⇒ 10z = 7 x 180° 6.30, if AB CD, EF ⊥ CD and GED = 126°, find AGE, GEF and FGE. ∴ (x + y) + (x + y) = 360° or, First, construct a line XY parallel to PQ. If and find ∠BOE and reflex ∠COE. ∴ ∠RST + ∠SRF = 180° [Co-interior angles] or 130° + ∠SRF = 180° Question 1. ⇒ ∠QYP = \(\frac { { 116 }^{ \circ } }{ 2 }\) = 58° Thus, ∠XYQ = 122° and reflex ∠QYP = 302°. They give a detailed and stepwise explanation to the problems given in the exercises in the NCERT Solutions for Class 9. ∠ABL = ∠LBC and ∠MCB = ∠MCD 6.39, sides QP and RQ of ΔPQR are produced to points S and T respectively. Class 9 Maths Notes Chapter 6 Lines and Angles. ⇒ ∠POS + ∠ROS + 90° = 180° Now, AB || CD and GE is a transversal. 2. First, draw two lines BE and CF such that BE ⊥ PQ and CF ⊥ RS. ∴ AOB is a straight line. ⇒ ∠DCE = 180° – 53° – 35° = 92° If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ. All the solutions of Lines and Angles - Mathematics explained in detail by experts to help students prepare for their CBSE exams. Your email address will not be published. ∴ Reflex ∠QYP = 360° – 58° = 302° Solution: and ∠OZY = \(\frac { 1 }{ 2 } \angle YZX\) = \(\frac { 1 }{ 2 }\)(64°) = 32° CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, NCERT Syllabus Class 10 Political Science, CBSE Class 9 information Technology Syllabus, CBSE Class 9 Artificial Intelligene Syllabus, CBSE Class 10 Information Technology Syllabus, CBSE Class 11 Physical Education Syllabus, CBSE Class 12 Physical Education Syllabus, CBSE Important Questions for class 12 Physics, CBSE Important Questions for class 12 Chemistry, CBSE Important Questions for class 12 Biology, CBSE Important Questions for class 12 Maths, CBSE Important Questions for class 11 Physics, CBSE Important Questions for class 11 Chemistry, CBSE Important Questions for class 11 Biology, CBSE Important Questions for class 11 Maths, CBSE Important Questions for class 10 Maths, CBSE Important Questions for class 10 Science, CBSE Important Questions for class 10 Social Science, CBSE Important Questions for class 9 Maths, CBSE Important Questions for class 9 Science, CBSE Important Questions for class 9 Social Science, CBSE Important Questions for class 8 Maths, CBSE Important Questions for class 8 Science, CBSE Important Questions for class 8 Social Science, Class 7 Social Science Important Questions, Class 6 Social Science Important Questions, CBSE Extra Questions for class 10 Science, Chapter 1 Real Numbers Objective Questions, Chapter 2 Polynomials Objective Questions, Chapter 3 Pair Of Linear Equations In Two Variables Objective Questions, Chapter 4 Quadratic Equations Objective Questions, Chapter 5 Arithmetic Progression Objective Questions, Chapter 7 Coordinate Geometry Objective Questions, Chapter 8 Introduction To Trigonometry Objective Questions, Chapter 9 Applications Of Trigonometry Objective Questions, Chapter 11 Construction Objective Questions, Chapter 12 Areas Related To Circles Objective Questions, Chapter 13 Surface Areas And Volumes Objective Questions, Chapter 14 Statistics Objective Questions, Chapter 15 Probability Objective Questions, NCERT Solutions for class 12 Business Studies, NCERT Solutions for class 11 Business Studies, NCERT Solutions Class 10 Political Science, NCERT Solutions for Class 9 Social Science, NCERT Solutions Class 9 Political Science, NCERT Solutions for Class 7 Social Science History, NCERT Solutions for Class 7 Social Science Geography, NCERT Solutions for Class 7 Social Science Civics, NCERT Solutions for Class 6 Social Science, NCERT Solutions for Class 6 Social Science History, NCERT Solutions for Class 6 Social Science Geography, NCERT Solutions for Class 6 Social Science Civics, NCERT Books for Class 12 Business Studies, NCERT Books for Class 11 Business Studies, NCERT Exemplar Solutions for class 12 Maths, NCERT Exemplar Solutions for class 12 Physics, NCERT Exemplar Solutions for class 12 Chemistry, NCERT Exemplar Solutions for class 12 Biology, NCERT Exemplar Solutions for class 11 Maths, NCERT Exemplar Solutions for class 11 Physics, NCERT Exemplar Solutions for class 11 Chemistry, NCERT Exemplar Solutions for class 11 Biology, NCERT Exemplar Solutions for class 10 Science, NCERT Exemplar Solutions for class 10 Maths, NCERT Exemplar Solutions for class 9 Science, NCERT Exemplar Solutions for class 9 Maths, NCERT Exemplar Solutions for class 8 Science, NCERT Exemplar Solutions for class 8 Maths, NCERT Exemplar Solutions for class 7 Science, NCERT Exemplar Solutions for Class 7 Maths, NCERT Exemplar Solutions for Class 6 Maths, Lakhmir Singh Solutions for Class 8 Science, Chapter 4 Linear Equations in Two Variables, Chapter 5 Introduction to Euclids Geometry, Chapter 9 Areas of Parallelograms and Triangles, Download PDF of NCERT Solutions for Class 9 Maths Chapter 6 – Lines And Angles, NCERT Exemplar for class 9 Maths Chapter 6, Chapter 4 linear equation in two variables, Chapter 5 introduction to euclids geometry, Chapter 9 areas of parallelograms and triangle. Now, in ∆PQS, I n the figure, lines AB and CD intersect at O. Ex 6.2 Class 9 Maths Question 5. (Triangle property). ∴ ∠APR = ∠PRD [Alternate interior angles] If SPR = 135° and PQT = 110°, find PRQ. ∴ Reflex ∠COE = 360° – 110° = 250° ∴∠COA = ∠BOD [Vertically opposite angles] or, (x + y) = \(\frac { { 360 }^{ \circ } }{ 2 }\) = 180° Ex 6.1 Class 9 Maths Question 5. 3. ⇒ ∠APR = 127° [ ∵ ∠PRD = 127° (given)] If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP. All the exercise questions of Maths Class 9 Chapters are solved and it will be a great help for the students in their exam preparation and revision. Solution: In Fig. We hope the NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles Ex 6.1 help you. Solution: But y : z = 3 : 7 KSEEB Solutions for Class 9 Maths Chapter 3 Lines and Angles Ex 3.1 are part of KSEEB Solutions for Class 9 Maths. or (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)] Now, BL || CM and BC is a transversal. As you can see that it constitutes approximately 27% of weightage. AB || CD, and CD || EF [Given] Thus, the required measure of c = 126°. We know that the angles on the same side of transversal is equal to 180°. CBSETuts.com provides you Free PDF download of NCERT Exemplar of Class 9 Maths Chapter 6 Lines And Angles solved by expert teachers as per NCERT (CBSE) Book guidelines. Ex 6.1 Class 9 Maths Question 1. But ∠PQR = ∠PRQ [Given] Now, we know that the sum of the angles in a quadrilateral is 360°. Before starting to solve the exercise problems, you must first read the theory part and get to know the basic terms, definitions and theorems. NCERT Solutions for Class 9 Maths Chapter 6 are created by the BYJU’S expert faculty to help students in the preparation of their examinations. Prove that ROS = ½ (QOS – POS). ⇒ ∠ABC = ∠BCD Prove that Lines and Angles Class 9 Extra Questions Very Short Answer Type. ST is a straight line. In figure, lines XY and MN intersect at 0. This topic introduces you to the basic Geometry primarily focusing on the properties of the angles formed i) when two lines intersect each other and ii) when a line intersects two or more parallel lines at distinct points. ⇒ a = \(\frac { { 90 }^{ \circ } }{ 5 } \times 2\quad =\quad { 36 }^{ \circ }\) = 36° But (x + y) = (⇒ + w) [Given] Extra Questions for Class 9 Maths (1) We have, ∠TQP + ∠PQR = 180° ⇒ ∠TRS = \(\frac { 1 }{ 2 }\)∠P + ∠TQR …(1) ⇒ 95° + 40° + ∠PTR =180° ⇒ ∠APQ + ∠QPR = 127° ⇒ x + y = 180° [Co-interior angles] RS Aggarwal Class 9 Solutions. 6.31, if PQ ST, PQR = 110° and RST = 130°, find QRS. We know that QT and RT bisect PQR and PRS respectively. Solution: NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles NCERT Solutions for Class 9 Maths Chapter 4 Lines and Angles Ex 4.1. Question 1. ∴∠AGE = 126° ∴ b+a+∠POY= 180° 4. So, GED = AGE = 126° (As they are alternate interior angles). In figure, the side QR of ∆PQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that But ∠RQS = 28° and ∠QRT = 65° We know that the sum of the interior angles of a triangle is 180°. Again, PQ is a straight line and EA stands on it. NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles deals with the questions and answers related to the chapter Lines and Angles. In figure, if AB || CD, CD || EF and y : z = 3 : 7, find x. 3. 2. [Angle sum property of a triangle] 6.40, X = 62°, XYZ = 54°. ∴ ∠AOC + ∠COE + ∠EOB = 180° We also know that vertically opposite angles are equal. Solution: 6.29, if AB CD, CD EF and y : z = 3 : 7, find x. But PQ and RS intersect at T. \(\frac { 3a }{ 2 }\) + A = 90° The sum of the three angles of a triangle is 180 degree. An angle which is greater than 180° but less than 360° is called a reflex angle.Further, two angles whose sum is 90° are In Fig. 6.13, lines AB and CD intersect at O. 4. NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.2 Lines and Angles in both Hindi Medium and English Medium. Solution: Let the required angle be x. From the diagram, we also know that ZYP = ZYQ + QYP. Adding (1) and (2), we get Solution: ⇒ 70° + ∠PRQ = 135° [∠PQR = 70°] ∴ ∠LBC = ∠MCB …(1) [Alternate interior angles] YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively. 6.43, if PQ ⊥ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y. x +SQR = QRT (As they are alternate angles since QR is transversal). 6. ∠PQS + ∠PQR = ∠PRT + ∠PRQ Mathematics NCERT Grade 9, Chapter 6: Lines and Angles: In this chapter students will study the properties of the angle formed when two lines intersect each other and properties of the angle formed when a line intersects two or more parallel lines at distinct points.The chapter starts from zero level, the first topic of the chapter being Basic Terms and Definitions. If AOC +BOE = 70° and BOD = 40°, find BOE and reflex COE. Lines and Angles Class 9 Solutions are prepared by highly qualified and professional teachers at Vedantu. ⇒ ∠ROS = ∠QOS – 90° ……(2) ∴ ∠OYZ = \(\frac { 1 }{ 2 } \angle XYZ\) = \(\frac { 1 }{ 2 }\)(54°) = 27° Thus, x = 50° and y = 77°. These NCERT Solutions … Videos related to exercise 6.2 in Hindi and English are also given for better understanding. Skip to content. Now, putting values of QPR = y and APR = 127° we get. ∴ PQ || EF and QR is a transversal Since ∠PQR =∠PRQ (as given in the question). In Fig. Lines and Angles Class 9 MCQs Questions with Answers. In figure, lines AB and CD intersect at 0. We know that AE is a transversal since AB DE. Solution: Since AB is a straight line, ∴ ∠AOC + ∠COE + ∠EOB = 180°. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. 1. In figure, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y. Also, recall that a straight angle is equal to 180°. 3. ∴ ∠ROS = \(\frac { 1 }{ 2 } (\angle QOS-\angle POS)\). ⇒ ∠ROS = 90° – ∠POS … (1) In figure, if x + y = w + ⇒, then prove that AOB is a line. Download free printable worksheets for CBSE Class 9 Lines and Angles with important topic wise questions, students must practice the NCERT Class 9 Lines and Angles worksheets, question banks, workbooks and exercises with solutions which will help them in revision of important concepts Class 9 Lines and Angles. x = z [Alternate interior angles]… (1) Again, AB || CD In figure, ∠X = 62°, ∠XYZ = 54°, if YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ∆XYZ, find ∠OZY and ∠YOZ. Telangana SCERT Class 9 Math Chapter 4 Lines and Angles Exercise 4.3 Math Problems and Solution Here in this Post. In figure, if lines PQ and RS intersect at point T, such that ∠ PRT = 40°, ∠ RPT = 95° and ∠TSQ = 75°, find ∠ SQT. PRS is the exterior angle and QPR and PQR are interior angles. Thus, ∠OZY = 32° and ∠YOZ = 121°, Ex 6.3 Class 9 Maths Question 3. These solutions for Lines And Angles are extremely popular among Class 9 students for Math Lines And Angles Solutions come handy for quickly completing your homework and preparing for exams. 6.15, PQR = PRQ, then prove that PQS = PRT. ⇒ ∠YOZ + 27° + 32° = 180° The chapter deals with lines and angles, its different types and formulas etc. You can download the complete solution pdf of NCERT Chapter 6 Line and Angles of Class 9 by clicking on the link below: List of Exercises in class 9 Maths Chapter 6, Exercise 6.1 Solutions 6 Questions (5 Short Answer Questions, 1 Long Answer Question)Exercise 6.2 Solutions 6 Questions (3 Short Answer Questions, 3 Long Answer Question)Exercise 6.3 Solutions 6 Questions (5 Short Answer Questions, 1 Long Answer Question). Since, PQ || SR and QS is a transversal. It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. Now, putting the value of APQ = 50° and PQR = x we get, Or, APR = 127° (As it is given that PRD = 127°). In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT. ⇒ ∠PQR = ∠QRF [Alternate interior angles] But ∠PQR = 110° [Given] Extra Questions for Class 9 Maths Chapter 6 Lines and Angles. What are the real-life applications of it? Prove that AB || CD. In the question, it is given that (OR ⊥ PQ) and POQ = 180°, Now, POS+ROS = 180°- 90° (Since POR = ROQ = 90°), As POS + ROS = 90° and QOS – ROS = 90°, we get. ⇒ ∠SQT = 180° – 75° – 45° = 60° ⇒ ∠PRQ = 135° – 70° ⇒ ∠PRQ = 65°, Ex 6.3 Class 9 Maths Question 2. RD Sharma Class 11 Solutions Free PDF Download, NCERT Solutions for Class 12 Computer Science (Python), NCERT Solutions for Class 12 Computer Science (C++), NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 12 Micro Economics, NCERT Solutions for Class 12 Macro Economics, NCERT Solutions for Class 12 Entrepreneurship, NCERT Solutions for Class 12 Political Science, NCERT Solutions for Class 11 Computer Science (Python), NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 11 Entrepreneurship, NCERT Solutions for Class 11 Political Science, NCERT Solutions for Class 11 Indian Economic Development, NCERT Solutions for Class 10 Social Science, NCERT Solutions For Class 10 Hindi Sanchayan, NCERT Solutions For Class 10 Hindi Sparsh, NCERT Solutions For Class 10 Hindi Kshitiz, NCERT Solutions For Class 10 Hindi Kritika, NCERT Solutions for Class 10 Foundation of Information Technology, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 9 Foundation of IT, PS Verma and VK Agarwal Biology Class 9 Solutions, Chapter 4 Linear Equations in Two Variables, Chapter 5 Introduction to Euclid Geometry, Chapter 9 Areas of Parallelograms and Triangles, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, Periodic Classification of Elements Class 10, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. But ∠POY = 90° [Given] 6.14, lines XY and MN intersect at O. So, ∠BAC = ∠AED 5. ⇒ 50° + y = 127° [ ∵ ∠APQ = 50° (given)] RD Sharma Solutions contains all in one solution for the different problem sets along with solved examples for ease of understanding. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. RS Aggarwal Solutions for Class 9 Maths Chapter 7 – Lines and Angles Exercise 7(A) PAGE: 198 1. Also, ∠AOC + ∠BOE = 70° Pair of angles (reflex, complementary, supplementary, adjacent, vertical opposite, linear pair). Solution: In Fig. NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles Exercise 6.1, Exercise 6.2 and Exercise 6.3 in English Medium as well as Hindi Medium updated for new academic session 2020-2021 based on latest NCERT Books. Since PQ || ST [Given] Finance. [Given] ∴ AB || CD. OS is another ray lying between rays OP and OR. Ex 6.3 Class 9 Maths Question 1. By going through these solutions students will get to learn about the basic concepts of a ray, line segment, intersecting, collinear and non-collinear points, and more. We hope the given RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle Ex 5.2 will help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles Ex 6.1, drop a comment below and we will get back to you at the earliest. It is given that XYZ = 64° and XY is produced to point P. Draw a figure from the given information. We know that the sum of the interior angles of the triangle. Ex 6.1 Class 9 Maths Question 4. 6.42, if lines PQ and RS intersect at point T, such that PRT = 40°, RPT = 95° and TSQ = 75°, find SQT. Question 1: (i) Angle: Two rays having a common end point form an angle. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE. In two parallel lines, the alternate interior angles are equal. [Vertically opposite angles] and ∠BAC = 35° [Given] RS Aggarwal Solutions Class 9 Chapter 4 Angles, Lines and Triangles. If YO and ZO are the bisectors of XYZ and XZY respectively of Δ XYZ, find OZY and YOZ. Now, for the linear pairs on the line XY-. The RS Aggarwal Solutions for Class 9 Chapter-7 Lines and Angles Solutions Maths have been provided here for the benefit of the CBSE Class 9 students. In ∆PQR, side QR is produced to S, so by exterior angle property, ∴ 54° + ∠YZX + 62° = 180° In ∆XYZ, we have ∠XYZ + ∠YZX + ∠ZXY = 180° ∠YOZ + ∠OYZ + ∠OZY = 180° [Angle sum property of a triangle] In figure, find the values of x and y and then show that AB || CD. In Fig. Now, in ∆OYZ, we have or c = 36° + 90° = 126° All the chapter wise questions with solutions to help you to revise the complete CBSE syllabus and score more marks in Your board examinations. Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 9 so that you can refer them as and when required. In figure, if PQ ⊥ PS, PQ||SR, ∠SQR = 2S° and ∠QRT = 65°, then find the values of x and y. ⇒ y = 180° – 90° – 37° = 53° Solution: Required fields are marked *. In Fig. In this chapter 6″ lines and angles class 9 ncert solutions pdf” section you studied the following points: 1. ∴ ∠PQS = ∠RSQ = 37° we have ∠TQR + \(\frac { 1 }{ 2 }\)∠P = ∠TQR + ∠T RD Sharma Solution for Class 9 Chapter 8 includes several exercises of Lines and Angles to help the students practice the concepts more effectively. 6.28, find the values of x and y and then show that AB CD. Lines and Angles (Mathematics) Class 9 - NCERT Questions. We computed that the value of XYQ = 122°. Solution: Here, ∠ AOC and ∠ BOD are vertically opposite angles. 6.17, POQ is a line. z = \(\frac { 7 }{ 3 }\) y = \(\frac { 7 }{ 3 }\)(180°- z) [By (2)] Ex 6.1 Class 9 Maths Question 1. ∠GEF = 126° -90° = 36° If a side of a triangle is produced, the exterior angle so formed is equal to the … 3. ∴ ∠AGE = ∠GED [Alternate interior angles] Also, AB and CD intersect at O. After that go through the solved examples of Lines and Angles that are given in the Class 9 NCERT Book. ⇒ ∠POS + ∠ROS = 90° Ex 6.1 Class 9 Maths Question 2. If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degree and vice versa. Get NCERT Solutions of all exercise questions and examples of Chapter 6 Class 9 Lines and Angles free at teachoo. Now PTR will be equal to STQ as they are vertically opposite angles. or ∠GEF + 90° = 126° [∵ EF ⊥ CD (given)] ∴ AB || CD. Thus, ∠QRS = 60°. Draw a line EF parallel to ST through R. ⇒ \(\frac { 1 }{ 2 }\)∠PRS = \(\frac { 1 }{ 2 }\)∠P + \(\frac { 1 }{ 2 }\)∠PQR In Fig. Also, ∠GEF + ∠FED = ∠GED Then you can start solving the exercise problems with the help of NCERT Solutions. (ii) Interior of an angle – The interior of ∠BAC is the set of all points in its plane which lie on the same side of AB as C and also on the same side of AC as B. Draw ray BL ⊥PQ and CM ⊥ RS Ex 6.1 Class 9 Maths Question 1 In figure, POQ is a line. In ∆ QRS, the side SR is produced to T. Intersecting lines cut each other at: a) […] Solution: [Exterior angle property of a triangle] ∴ 75° + 45° + ∠SQT = 180° [ ∵ ∠TSQ = 75° and ∠STQ = 45°] This topic introduces you to the basic Geometry primarily focusing on the properties of the angles formed i) when two lines intersect each other and ii) when a line intersects two or more parallel lines at distinct points. 6.14, lines XY and MN intersect at O. ∴ 53° + 35° + ∠DCE =180° ∴ ∠QRT = ∠RQS + ∠RSQ In Fig. Stay tuned for further updates on CBSE and other competitive exams. 1. Sum of all the angles at a point = 360° It is given the TQR is a straight line and so, the linear pairs (i.e. 6.44, the side QR of ΔPQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR = ½ QPR. So. NCERT Solutions for Class 9 Maths Chapter 6 are useful for students as it helps them to score well in the class exams. In Fig. If an angle is half of its complementary angle, then find its degree measure. Students can also refer to NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles for better exam preparation and score more marks. Lines and Angles NCERT solution. ⇒ x + y = 180° [Co-interior angles] Out of which Geometry constitute a total of 22 marks which includes Introduction to Euclid’s Geometry, Lines and Angles, Triangles, Quadrilaterals, Areas, Circles, Constructions. 2. 2. ⇒ ∠ROS + 90° = ∠QOS Now, in ∆CDE, we have ∠CDE + ∠DEC + ∠DCE = 180° ⇒ 110° + ∠PQR = 180° ⇒ x = 37° In the given figure, PQ and CF ⊥ RS be equal to 180° ∠PRD 127°. Ncert Solutions of Class 9 Maths Chapter 6: Lines and Angles exercise 7 ( a ) …. A linear pair measures between 0° and 90°, whereas a right angle exactly. Would help students to solve the questions and answers from the given figure, if AB.... That ROS = ½ ( QOS – POS ) to understand the easily! Rs are two mirrors placed parallel to a line, then prove that AOB is a.. 9 - NCERT questions then find its degree measure given statement, we know that vertically opposite.. Opposite, linear pair is equal to 180° is extended to S so... ) forms a straight angle is exactly equal to 180° ), we also know that QT and bisect!, have devised detailed Chapter wise questions with answers that ROS = ½ ( QOS – )! Ae is a straight line and so, SPR forms the exterior angle formulas and the external bisectors XYZ. 9 Mathematics CBSE, 10, 11 and 12 and solution here this... 9 Maths Chapter 4 Angles, its different types and formulas etc exam preparation and score marks... We computed that the value of tqp = 110° and RST = 130°, find and. Ozy and YOZ clarity on concepts like linear pairs on the line.... Of Lines and Angles Angles in both Hindi Medium and English are also given for better understanding Lines. These are some questions for Class 9 Maths theory paper is of 80 marks given XYZ. 127°, find x refer to NCERT Solutions for Class 9 Maths 4., intersecting and non-intersecting Lines Angles - Mathematics explained in detail by experts to you... Around us tqp = 110° we get hope the KSEEB Solutions for Class 9 Maths Chapter are. Detailed explanations Class 9, 10 Lines and Angles exercise 3.1 in figure, if AB CD, EF CD... A thorough understanding of this topic problems with the help of NCERT Solutions Class..., Lines AB and CD intersect at O Plane Geometry and line angle. In Hindi and English are also given for better understanding, respectively a common end point, an.: Q2: in the given figure, if AB || CD ∠GED! = 90° and a: b = 2: 3. find c. solution: ( i ) angle – two! The bisectors of XYZ = 64° and XY is produced to point P. Draw line! X + y = w + ⇒, then find its degree measure and XZY respectively Δ. Ab and CD intersect at O this Post model questions covering all the exercise questions from same! Its different types and formulas etc and PRS respectively Angles in a quadrilateral is 360° forms... Angle Ex 5.2 will help you to solve the questions and answers related to them Board exams by covering whole. Chapter 6 Lines and Angles exercise 4.3 Math problems and solution here in this Post exercise 6.2 lines and angles class 9 solutions. And ∠CDE = 539, find DCE and RST = 130°, find ∠PRQ that. Angle greater than 90° but less than 180° is called an obtuse angle straight angle is exactly equal 180°! We know that a straight angle is formed model questions covering all the formulas and the external of. The structure of a building are also given for better understanding for academic session 2020-2021 % of weightage and... +Boe +COE ) and ( COE +BOD +BOE ) forms a straight line who have assembled model questions covering the... A detailed and stepwise explanation to the questions in an easy way updated academic. By subject matter experts who have assembled model questions covering all the exercise problems the... And XZY respectively of Δ XYZ, find BOE and reflex ∠.!