Class 9 Maths Lines and Angles Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. [sum of all the angles of a triangle is 180°] Solution: We have created Step by Step solutions for Class 9 maths to help you to revise the … Solution: Solution: A triangle cannot have two obtuse angles. Let one of interior angle be x°. NCERT Exemplar for Class 9 Maths Chapter 7 With Solution | Triangles Hence, the above equation can be written as: Therefore, option (C) is the correct answer. 3. 4. While practising the model solutions from this chapter, you will also learn to use the angle sum property of a triangle while … OS is another ray lying between rays OP and OR. NCERT solutions for class 9 Maths is available to download for free from the links below. Bisectors of interior ∠B and exterior ∠ACD of a  ΔABC intersect at the point T. Prove that ∠BTC = ½ ∠BAC. 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Solution: In Fig. Class 9 Maths Chapter 6 Lines and Angles Exercise 6.3 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Here, ∠1 = ∠3 [vertically opposite angles] Answers to each question has been solved with Video. Download BYJU’S-The learning app to get personalized videos teaching various concepts of Maths such as lines and angles and of related topics with the help of pictures and video contents. Justify your answer. Can a triangle have two obtuse angles? => 180° /2 If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be Given In the figure, OD ⊥ OE, OD and OE are the bisectors of ∠AOC and ∠BOC. 3. Value of x + y should be 180o for ABC to be a line. No. ∴ ∠AOB = 180° Download the NCERT Exemplar Problem Solutions for Class 9 Maths Chapter 6 - Lines and Angles solved by Mathematics Expert Teachers at Mathongo.com as per CBSE (NCERT) Book guidelines. x° = 105°/2 You should get good marks in Class 9 examinations as it will always help you to get good rank in school. The type of questions that will be asked from NCERT Class 9 Maths Unit 6 are displayed in the below provided NCERT Exemplar Class 9 Maths Unit 6. 2. NCERT Exemplar Class 9 Maths Solutions Triangles Exercise 7.1: Multiple Choice Questions (MCQs) Question 1: Which of the following is not a criterion for congruence of triangles? We know that the sum of all the interior angles of a triangle should be = 180o. Write the correct answer in each of the following: 1. Now, ∠3 + ∠6 = 60° + 120° Is it necessary that each of these angles will be a right angle? Angles of a triangle are in the ratio 2:4:3. Substituting the value of x, x = 12, in 5x, 3x and 7x we get. 2. (a) 37 ½°                  (b) 52 ½°               (c)72 ½°               (d) 75° ⇒ If the sum of two adjacent angles is 180°, then a ray stands on a line. Let two intersecting lines l and m makes a one right angle, then it means that lines I and m are perpendicular each other. Solution: Hence, l || m. Question 5: The smallest angle of the triangle is ∠PAB =∠ABQ Therefore, option (A) is the correct answer. NCERT Class 9 Maths Lines And Angles Questions. If two lines intersect, prove that the vertically opposite angles are equal. Show that the lines m and n are parallel. Show that ∠ABC = ∠DEF. Solution: No triangle can be drawn having its angles 45°, 64° and 72°. ∠QRS = ∠QRA + ∠ARS (ii), the sum of two interior angles 73° + 106° = 179° ≠ 180°. If the triangle has two obtuse angles, then there are two angles which are at least 91° each. 2x° = 105° ∠C = 3x = 3 x 20° = 60° Question 4: Infinitely many triangles can be drawn having its angles as 53°, 64° and 63°. Download the NCERT Exemplar Problem Solutions for Class 9 Maths Chapter 6 - Lines and Angles solved by Mathematics Expert Teachers at Mathongo.com as per CBSE (NCERT) Book guidelines. NCERT Exemplar for Class 9 Maths Chapter 6 With Solution | Lines and Angles. 6.9, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. Similarly, the ray DO lies on the line AOB. NCERT Exemplar Class 9 Maths Unit 6 Lines and Angles. Question 5: Therefore, option (D) is the correct answer. => ∠AOC+ ∠COB = 2 x 90° [∴ OD ⊥ OE] So, alternate interior angles are equal. 5. Proof Since, m || n and p is perpendicular to m and n. Solution: No, since, lines l and m are perpendicular to the line n. Students who are in Class 9 or preparing for any exam which is based on Class 9 Maths can refer NCERT Book for their preparation. Again, let n and p be another two lines which are perpendicular to the intersecting lines meet at point D. => ∠AOC + ∠COB= 2 ∠DOE NCERT Exemplar Class 9 Mathematics Chapter 6 Lines and Angles, is provided in pdf format for students to prepare for exams. ½ ∠EAB =½ ∠ABH    [dividing both sides by 2] So, sum of two interior angles is supplementary. Basic terms like line-segment, collinear points, non-collinear points, … Solving Latest year 2021 Exemplar Problems Solutions for Class 9 Lines and Angles is the best option to understand the concepts given in NCERT books and do advanced level preparations for Class 9 exams. To show ∠ABC = ∠DEF. Prove that the bisectors of any pair of corresponding angles so formed are parallel. Question 2: Give reason for your answer. Solution: Given, ∠A = ∠B+∠C …(i) 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to. Solution: Also download revision worksheets and easy to learn study notes, prepared based on NCERT and CBSE guidelines. Since all the angles are less than 90o, the triangle is an acute angled triangle. Given In the figure ∠1 = 60° and ∠6 = 120° Suppose two angles are ∠B = 90° and ∠C = 90°. In the figure, find the value of x for which the lines l and m are parallel. Solution: Question 9: ∠DEF = ∠DPC …(eq.1) [Corresponding angles]. Solution: (b) an obtuse angled triangle To prove ΔABC must have two acute angles Solution: By Preparing Exercise wise Exemplar Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams. By Preparing Exercise wise Exemplar Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams. NCERT Exemplar Class 9 Mathematics Chapter 6 Lines and Angles, is provided in pdf format for students to prepare for exams. Hence, the smallest angle of a triangle is 40°. In figure, if AB || CD || EE, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to No, a triangle cannot have all angles less than 60°, because if all angles will be less than 60°, then their sum will not be equal to 180°. Solution: A transversal intersects two parallel lines. (a) 40°              (b) 50°                (c) 60°                          (d) 70° EF be the transversal passing through the two parallel lines at P and Q respectively. No, because each of these will be a right angle only when they form a linear pair. Justify your answer. This subject acquaints you with the essential Geometry principally focusing on the properties of the angles shaped I) when two lines converge one another and ii) when a line meets at least two equal lines at particular focuses. 2. x + 44° = 180° Exercise 6.2: Very Short Answer Type Questions. Therefore, infinitely many triangles can be drawn having its angles as 53°, 64° and 63°. To show Points A, O and B are collinear i.e., AOB is a straight line. SOLUTION: POQ is a straight line. Theorem videos are also available.In this chapter, we will learnBasic Definitions- Line, Ray, Line Segment, Angles, Types of Angles ∠C = 3x , ∠A+∠B+ ∠C= 180° ∠BAC + ∠ACB + ∠ABC = 180° and ∠C =7x = 7 x 12° = 84° x = 180°-44° We know that, if a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel. Understanding of Maths concepts as per the CBSE exam pattern 180°, then the sum of two interior angles 180°... If the sum of two interior opposite angles are equal ncert Book for Class 9 Maths all available... ∠Q > ∠R, PA is the bisector of ∠AOC and ∠BOC respectively Exercise wise Exemplar questions Solutions. Atleast two acute angles proof let us take 59o, which is the correct answer in each of two. 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