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RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4) Exercise 8.4

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Last updated date: 20th May 2024
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RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4) Exercise 8.4 - Free PDF

Free PDF download of RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles Exercise 8.4 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 8 - Lines and Angles Ex 8.4 Questions with Solutions for RD Sharma Class 9 Maths are provided to help you to revise complete Syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

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Competitive Exams after 12th Science

Lines and Angles

Lines and angles are the basic terms that set up the basic foundation for geometry as a whole.


A line is defined as a row of closely placed dots that extends in two opposite directions in an infinite manner. The line has only one single dimension which is its length. The mathematician Euclid defined line as a breadthless length. In a standard cartesian plane, a line can be denoted by the linear equation which is of the form ax + by = c. 


Rays can be defined as the lines with one end as its starting point and the other end extending upto infinity. Rays only extend in one single direction without any end. When two rays are joined end to end, an angle is formed. 


An angle is defined as something created when two rays meet at a particular endpoint. Angles are usually measured in degrees using a device called a protractor. All geometric shapes have lines and angles in them. An angle can have any value between 0 degrees to 360 degrees. 


Types of Lines

Depending upon their properties, lines can be of different types: 

Horizontal line: These are the types of lines which when in a cartesian plane are parallel to the x-axis and perpendicular to the y-axis. In other words, it makes 0 degrees angle with the x-axis and 90 degrees with the y-axis. 


Vertical line: These are the types of lines which when in a cartesian plane are parallel to the y-axis and perpendicular to the x-axis. In other words, it makes 0 degrees angle with the y-axis and 90 degrees with the x-axis. 


Parallel lines: A pair of lines which are moving alongside with a constant distance between each other at any given point are called parallel lines. They make a 0 degree angle. 


Perpendicular lines: When two lines touch each other at an angle of 90 degrees, they are known as perpendicular lines. 


Transversal lines: When a common line intersects two lines at two different respective points, the whole system is called transversal lines. 

Types of Angles

Angles are of different types. They can be divided based on their measurements. There are six types of angles based on measurements,they are:

Acute angle: It is an angle in which the measurement of an angle is less than 90 degrees.


Obtuse angle: It is an angle in which the measurement of an angle is greater than 90 degrees and less than 180 degrees.


Right angle: It is an angle in which the measurement is equal to 90 degrees.


Straight Angle: It is an angle in which the measurement is equal to 180 degrees.


Reflex angle: It is an angle in which the measurement of an angle is greater than 180 degrees and less than 360 degrees.


Complete angle: It is an angle in which the measurement is 360 degrees.

FAQs on RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4) Exercise 8.4

1. What are the properties of a line mentioned in RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4)?

Since there are different kinds of lines in geometry, each of them has different kinds of properties. However, there are some common properties of lines that can be listed.


Properties of Lines:

  • A line can be defined as a set of an endless number of points placed closely to each other.

  • They extend infinitely in both directions of their points.

  • Lines are one-dimensional and do not have any depth, breadth or thickness.

2. What are the properties of an angle mentioned in RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4)? 

Since there are different kinds of angles in geometry, each of them has different kinds of properties. However, there are some common properties of angles that can be listed.


Properties of Angles

  • An angle is formed when two rays join each other at a point in the same plane.

  • The rays forming the angle are called arms of the angle and the point at which the two rays meet to form an angle is called the vertex. Refer to the Vedantu website or app for an elaborate and easy explanation.

3. Are linear pairs of angles always congruent?

Linear pairs of angles necessarily are not always congruent. When the measure of each of the angles is 90 degrees, only then linear pairs of angles are considered to be congruent. But, linear pairs of angles can always be supplementary.

4. What is a line segment according to RD Sharma Class 9 Solutions Chapter 8 - Lines and Angles (Ex 8.4)?

A line segment is merely a part of a line. It has two fixed end points, a fixed length and measurement. The length of a line segment can be measured in metric units such as millimetres, centimetres or other customary/standard units like foot or inches.

5. What are all the geometric tools one can use while studying lines and angles?

While studying lines and angles, students can use tools like ruler, compass, protractor, divider, set squares etc.