# RD Sharma Class 9 Chapter 8 Solutions (Lines and And Angles)

RD Sharma Class 9 Maths Solutions for Chapter 8** ‘**Lines and Angles**’**comprises solutions to all the problems given in the exercises of the chapter. These solutions will help you with the basic definitions of lines and angles. In this chapter of RD Sharma Solutions, you will learn about axioms and theorems with respect to angles, angle relations, the difference between the linear pair of angles and supplementary angles, and vertically opposite angles. The angles made by a transversal intersecting two parallel lines; and the properties of consecutive interior angles and alternate interior angles are also covered in this chapter.

There are 4 exercises in this chapter consisting of 33 questions with an additional set of 6 questions in the VSAQs exercise. The questions are broad ranging from evaluation of angles in some cases to proving several important theorems that will be used in other chapters of geometry. The questions in this chapter are arranged in an increasing order of difficulty to make your understanding compatibility with the complexity of the topics. You will learn how to manage your time effectively in the high-pressure surroundings in your exam hall. Practising the exercise questions thoroughly will help you in scoring good marks in your school exams.

At Instasolv, our experts have prepared the answers in line with comprehensive research on the frequently occurring doubts in lines and angles. RD Sharma Class 9 Maths Solutions for Chapter 8 are written in a simple language to make the most difficult questions easy to understand. Our team of expert mathematicians is dedicated to helping you in building a robust foundation for geometry for the higher classes. It is highly recommended that you rely on the Instasolv platform a source of reference for your homework for a better conceptual understanding of the Class 9 RD Sharma for Class 8.

## Introduction to Important Terms of Lines and Angles

- Line Segment: The part of the line which has two ends. A line segment is terminating in nature.
- Ray: A ray has one terminating end while the other end of the ray extends indefinitely.
- Collinear points: If we consider three points that lie on the same line, these 3 points are termed as collinear points; else these points are non-collinear to one another.
- Angle: An angle is formed where the terminating ends of two rays meet. Their point of intersection is called the vertex of the angle and the rays are termed the arms of the angle.
- Complementary angles are the pair of angles whose sum is 90° whereas supplementary angles are the pair of angles whose sum is 180°
- There are 3 conditions for two angles to be adjacent: they should have a common aim and a common vertex and the uncommon arms should not be on the same side of the common arms.
- Linear pair is formed when the uncommon arms make up a straight line such that their sum is 180°

**Important Axioms**

**Axiom 1: **If we consider a ray starting from a line, the adjacent angles will have a sum equal to 180°. Hence, these angles are supplementary.

**Axiom 2: **If we find that the sum of any two adjacent angles is 180°, then the uncommon arms on both sides of the common arms together form a straight line. That is the uncommon arms will make a linear pair of angles.

**Axiom 3: **This is the corresponding angles axiom. According to this, all pairs of corresponding angles are equal in the event of a transversal intersecting two parallel lines.

**Axiom 4: **If a transversal intersects a pair of lines so that the corresponding angles are equal, then it is a pair of parallel lines.

**Important Theorems**

- In the event of the intersection of two parallel lines by a transversal:

- The pairs of vertically opposite angles are equal.
- All pairs of alternate interior angles are equal
- All pairs of interior angles on the same side of the transversal are supplementary.

- Two lines that happen to be parallel to the same line are parallel to one another.
- Angle Sum Property: The sum total of all the angles in a triangle is 180°. This is also known as the angle sum property of a triangle.
- If a transversal intersects a pair of lines and the alternate angles so formed are equal, then the lines are parallel.
- If a transversal intersects a pair of lines and interior angles on the same side of the transversal are supplementary, then the two lines are parallel.

### Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 8: Lines and Angles

- Exercise 8.1 constitutes a set of 7 questions based majorly on the concepts of supplementary and complementary angles.
- In exercise 8.2, there are 10 questions in which you will be required to evaluate the value of the angles based on properties of the linear pairs of angles and adjacent angles.
- There are 6 questions in exercise 8.3 based on the property of vertically opposite angles.
- In 8.4, all the questions are based on a transversal intersecting 2 parallel lines and their properties.
- In the VSAQs exercise, there are theoretical questions and fill in the blanks exercises based on the theorems of parallel lines.

## Benefits of RD Sharma Solutions for Class 9 Chapter 8: Lines and Angles

- The answers for all exercise questions of RD Sharma Class 9 Maths Solutions Class 9 Maths Chapter 8 prepared by our experts are precise and on-point.
- We have mentioned detailed reasons at every step which will help you in memorising the theorems and axioms of lines and angles easily.
- The solutions at the Instasolv platform are free of cost and easily accessible.
- We have indexed the questions in each exercise systematically, so it will be a hustle-free task to quickly get your doubt addressed.