ALLEN Coaching
ApplyRegister for ALLEN Scholarship Test & get up to 90% Scholarship
Have you ever looked at a long, straight road with no visible ending into the distance and wondered where it might end? Or noticed the hands of a clock at exactly 3 o’clock forming a perfect 90-degree angle? These are everyday examples where we unknowingly observe lines and angles around us. In class 9 Maths NCERT chapter 6, students will study lines, angles and their properties. The purpose of this article is to make learning easier for students and explain the NCERT Solutions thoroughly.
Careers360 experts, experienced in this area, prepared the Class 9 NCERT solutions for lines and angles and adhered to the latest CBSE syllabus. There are various applications of lines and angles in our daily lives. So, having the concepts clear will be beneficial not only for the Class 9 board exams but also for day-to-day life. After going through all the NCERT Solutions for Class 9 Maths, students can practice the NCERT Exemplar Solutions Class 9 NCERT Maths Chapter Lines And Angles for a deeper understanding of the concepts. Along with this, using the NCERT Solutions for Class 9, learners can practise diagram-based questions and prove angle-based properties confidently.
Types of Angles:
Acute Angle: An acute angle measures between 0° and 90°.
Right Angle: A right angle is exactly equal to 90°.
Obtuse Angle: An angle that is greater than 90° but less than 180°.
Straight Angle: A straight angle is equal to 180°.
Reflex Angle: A reflex angle is greater than 180° but less than 360°.
Complementary Angles (x, y): x + y = 90°
Supplementary Angles (x, y): x + y = 180°
Adjacent Angles:
Adjacent angles are two angles that share a common side and a common vertex (corner point) without overlapping.
Linear Pair:
A linear pair of angles is formed when two lines intersect. Two angles are considered linear if they are adjacent angles formed by the intersection of two lines. The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.
Vertically Opposite Angles:
Vertically opposite angles are formed when two lines intersect at a point. Vertically opposite angles are always equal.
Transversal:
A transversal is a line that intersects two or more given lines at distinct points. It is used to create various types of angles, including:
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Interior Angles on the Same Side of the Transversal
Class 9 Maths Chapter 6 Question Answer: Exercise: 6.1 Total Questions: 6 Page number: 76-77 |
Question 1: In Fig. 6.13, lines AB and CD intersect at O. If
Answer:
Given that,
AB is a straight line. Lines AB and CD intersect at O.
Since AB is a straight line,
[since
So, reflex
It is given that AB and CD intersect at O.
Therefore,
Also,
So,
Question 2: In Fig. 6.14, lines XY and MN intersect at O. If
Answer:
Given that,
Line XY and MN intersect at O and
Also,
Since XY is a straight line
Therefore,
Thus, from eq (i) and eq (ii), we get,
So,
Since
Question 3: In Fig. 6.15,
Answer:
Given that,
ABC is a triangle such that
Now,
Similarly,
Equating the equation (i) and eq (ii), we get,
Therefore,
Hence, it is proved.
Question 4: In Fig. 6.16, ifx + y = w + z, then prove that AOB is a line.
Answer:
Given that,
It is known that the sum of all the angles at a point =
From eq (i) and eq (ii), we get,
Hence, proven that AOB is a line.
Answer:
Given that,
POQ is a line, OR
Now,
and,
Adding the eq (i ) and eq (ii), we get,
Hence, proved.
Answer:
Given that,
Now, XYP is a straight line.
So,
Thus reflex of
Since
[
Class 9 Maths Chapter 6 Question Answer: Exercise: 6.2 Total Questions: 5 Page number: 80-81 |
Question 1: In Fig. 6.29, if AB
Answer:
Given AB || CD and CD || EF and
Therefore, AB || EF and
Again, CD || AB
Putting the value of
Then
By equation (i), we get the value of
Question 2: In Fig. 6.30, if AB
Answer:
Given AB || CD, EF
In the above figure,
GE is transversal.
So, that
[Alternate interior angles]
Also,
Since AB is a straight line.
Therefore,
So,
Answer:
Draw a line EF parallel to the ST through R.
Since PQ || ST and ST || EF
Again,
Thus,
Question 4: In Fig. 6.32, if AB
Answer:
Given, AB || CD,
PQ is a transversal.
So,
Again, PR is a transversal.
So,
Answer:
Draw a ray BL
Since PQ || RS (Given)
So, BL || CM and BC is a transversal.
It is known that angle of incidence = angle of reflection
So,
Adding equations (i) and (ii), we get,
Both the interior angles are equal
Hence AB || CD
Question: In the figure,
Answer:
Given:
It means a° + b° = 180°..................(i)
And, a° - b° = 90° ..................(ii)
Now, add (i) and (ii), We get;
2 a° = 270°
Therefore, a° = 135°
And, thus b° = 180° - 135° = 45°
1. Understand different types of angles: Acute, obtuse, straight, reflex, and right angles need revision as a starting point to understand angle relationships in lines.
2. Learn angle pair relationships: Students need to understand complementary angles along with supplementary angles, whereas adjacent angles and linear pairs and vertically opposite angles are necessary for solving angle problems.
3. Know the angle properties of intersecting lines: When two lines intersect, the resulting vertically opposite angles will always be equal in measure to each other.
4. Apply properties of parallel lines with a transversal: You will discover the required behaviours of alternate interior angles, corresponding angles, and consecutive interior angles in cases where parallel lines intersect with a transversal.
5. Use angle theorems for reasoning and proof: When proving lines parallel, it is essential to use angle theorems, especially the “If two lines are parallel, alternate interior angles are equal” theorem, together with its converse proof.
6. Solve problems step-by-step using angle relationships: The solution of angle-based questions progresses easily through known angle pairs combined with postulates to create exact answers.
These are links to the solutions of other subjects, which students can check to revise and strengthen those concepts.
Before planning a study schedule, always analyse the latest syllabus. Here are the links to the latest NCERT syllabus and some of the important books that will help students in this cause.
Pair of angles, Parallel and Transversal Lines, Angle sum property of a triangle are the important topics covered in this chapter. Students can practice NCERT solutions for ch 6 maths class 9 to command these concepts.
There are 15 chapters starting from the number system to probability in the CBSE class 9 maths. which are listed below
Here you will get the detailed NCERT solutions for class 9 maths. For ease students can study lines and angles class 9 pdf both online and offline mode. practicing these solutions help them indepth understanding the cocepts which ultimately lead to score well in the exam.
Admit Card Date:17 April,2025 - 17 May,2025
Exam Date:01 May,2025 - 08 May,2025
Register for ALLEN Scholarship Test & get up to 90% Scholarship
Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters