RD Sharma Class 7 Maths Solutions Chapter 14 - Lines and Angles

In this Chapter 14 - Lines and Angles, several exercise questions with solutions for RD Sharma Class 7 Maths are given to help the students and understand the concepts better. 

Important Concepts of the Chapter

Following are some of the important concepts that are being discussed in this chapter:

• Introduction to Lines and Angles

• Related angles

• Complementary Angles

• Supplementary Angles

• Adjacent Angles

• Linear Pair

• Vertically Opposite Angles

• Pairs of Lines

• Intersecting Lines

• Transversal

• Angles made by a Transversal

• Transversal of Parallel Lines

• Checking for Parallel Lines

Introduction to Lines and Angles

It is really essential for us to thoroughly understand angles. We observe several angles in our day to day life. For example, foods like a slice of pizza or cake or nachos, have angles. Alphabets have angles like ‘L’ has a right angle. The hands of a clock make angles between them.

A plethora of other examples can be provided where lines and angles are applied. 

Let us familiarise ourselves with some important terms and definitions related to lines and angles:

• Line segment-A part of a line that has two endpoints is called a line segment.

• Ray-A part of a line with one endpoint is called a ray.

• Collinear points-When three or more points lie on the same line, then they are called collinear points.

• Non-collinear points-If three or more points do not lie on the same line, they are called non-collinear points.

• Angle-When two rays originate from the same endpoint, an angle is formed.

• Vertex-The rays making an angle are called the arms of the angle and the endpoint is called the vertex of the angle. 

• The acute angle-An acute angle is an angle that measures between 0° and 90°

• The right angle-An angle that is exactly equal to 90°, is a right angle. 

• The obtuse angle-An angle that is greater than 90° but less than 180° is called an obtuse angle.

• The straight angle-An angle that is equal to 180°, is a straight angle. 

• Reflex angle-An angle that is greater than 180° but less than 360° is called a reflex angle. 

Related Angles

• Complementary Angles-  When two angles have a sum of 90°, they are called complementary angles. In that case, we can say that one angle is complementary to the other angle.

• Supplementary Angles- When two angles have a sum of 180°, they are called supplementary angles. Therefore, we can say that one angle is supplementary to the other angle.

• Adjacent Angles-When two angles are adjacent, they have a common vertex and a common arm. The non-common arms will be on different sides of the common arm. Furthermore, the angle formed by the two non-common arms will always be equal to their sum.

• Linear Pair- When the sum of two adjacent angles is 180°, they are called a linear pair of angles.

• Vertically Opposite Angles-When, two lines intersect each other at a point, vertically opposite angles formed. There will always be two pairs of vertically opposite angles.

Pairs of Lines

• Intersecting Lines- When two lines touch or meet at one point, then they are called intersecting lines. Here, the touching point is called the point of intersection.

• Transversal- A line that intersects or meets two or more lines at distinct points is called a transversal.

• Angles made by a Transversal-We can find eight types of different angles with the lines when two lines act as transversal. All angles are distinct from one another. There are interior, exterior, adjacent angles and corresponding angles.

• Transversal of Parallel Lines- When a transversal cuts two parallel lines, every pair of corresponding angles and alternate interior angles are equal. Moreover, the pair of interior angles on the side of the transversal are supplementary to each other. Thus, a mere intersection can produce several angles and alter their properties.

Checking for Parallel Lines

We learned how to find different angles based on the lines. Now, we will learn about how the lines are based on the angles formed. If two lines are represented by the transversal and the corresponding angles are equal, then the lines are said to be parallel to each other.

Conditions for Lines to be Parallel

For two lines to be parallel, when a transversal cuts two lines any one of the following conditions must be fulfilled:

• When corresponding angles are equal.

• When alternate angles are equal.

• When the interior angles on the same side of the transversal are supplementary.