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Chapter 5

Lines and Angles

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The fifth chapter in Maths, for Class 7 is lines and angles. It talks about the various concepts and learnings about lines and angles. You can find the detailed explanations and solutions for the chapter in this article that will help you with the various aspects. The NCERT solutions for class 7 maths chapter 5 help students prepare with chapter-wise differentiation so that students can go through each subject more conveniently. It also provides all solutions to questions asked in the prescribed textbook. 

NCERT solutions provide constructed study material that helps students improve their scores and understand the subjects more deeply. The solutions also help students access several questions, including match the following, fill in the blanks, descriptive questions, and true or false. 

The NCERT solutions of chapter 5 will provide you with the knowledge about lines and angles; different types of angles, complementary angles, adjacent angles, linear pairs, various pairs of lines, which helps students understand the various angles of geometry in maths.

NCERT solutions for Class 7 Maths - Chapter 5 Lines and Angles

Under this chapter, students will learn the basic terms of lines and angles which set up the foundation for the subject. As we know the line segment has two endpoints and a ray has only one endpoint. Where two lines meet an angle is formed.

Let us take a look at the most important topics of Chapter 5 lines and angles. The important topics are listed as follows:

    • 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

    • Properties of lines and angles

The concept of lines was introduced by ancient mathematicians, meant to represent straight objects with negligible width and depth. In geometry, lines and angles form the basic shapes. Lines are figures that are made up of infinite points that will always extend indefinitely in any direction. There are many types of lines such as intersecting lines, perpendicular lines, transversal lines, etc. 

An angle is formed when two lines meet at a common point. The most practical shapes of mathematics are the geometrical shapes which are mostly taught in class 7. There are many types of angles: complementary angles, adjacent angles, vertically opposite angles, supplementary angles, etc.

  • Related angles

    •  Complementary Angles:

 The angles whose measures add up to 90 degrees are called complementary angles. These two angles need not be         adjacent to be complementary. The complementary angles always appear in pairs. These angles can be part of the         same or different figures. 

    • Supplementary Angles:

The two angles that add up to 180 degrees are called supplementary angles. The supplementary angles always form a straight line when they meet at 180 degrees. These angles can either be adjacent or nonadjacent. The angles with the common vertex and common arm are called supplementary adjacent angles. Whereas the angles with different vertices and arms are called non-adjacent supplementary angles. 

    • Adjacent Angles: 

The angles which do not overlap and always have a common vertex and arm are called adjacent angles. Such angles share a common vertex but do not share a common side. The two adjacent angles can either be supplementary or complementary, based on their sum of value.

    • Linear Pair:

When the two lines intersect each other at a single point they form a linear pair of angles. After the intersection, if the angles are adjacent to each other are said to be linear. The sum of linear pair angles is always equal to 180 degrees. 

    • Vertically Opposite Angles

The angles which are opposite each other are called vertically opposite angles. Such angles are opposite each other at a specific vertex. These angles are created by two intersecting lines and are also called vertical angles.

  • Pairs of Lines 
    • Intersecting Lines: 

Two or more lines which intersect each other at a common point are called intersecting lines. The point where they intersect each other is known as the point of intersection.

    • Transversal lines: 

When two lines intersect in the same plane at two distinct points it is called a transversal line. The intersection caused by a transversal line forms several angles. The transversal lines always connect the two parallel lines.

    • Angles made by a Transversal:

Through transversal lines, when two parallel lines intersect it forms eight angles such as corresponding angles, alternate exterior angles, alternate interior angles, and co-interior angles. When a transversal cuts the two or more lines, the angles which occupy the same relative position are the corresponding angles. 

    • Transversal of Parallel Lines:

When the lines are parallel, the corresponding angles are congruent.  If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.

    • Parallel lines:

The lines which do not meet at any point in a plane and also do not intersect each other are called parallel lines. These lines have two starting points and an ending point.

    • Perpendicular lines 

The lines are said to be perpendicular when they form a right angle with each other and also meet at a single point. Such lines are opposite to each other.

  • Properties of lines and angles:

In geometry, lines and angles have their properties which are based on points, vertices, arms, rays, etc.

  • Properties of lines:

    • A set of three or more points that lie on the same line are collinear points.

    • Non-collinear points do not lie on the same line. 

    • The three points can be either collinear or non-collinear.

    • The collinear or non-collinear points do not lie together at the same line or point. 

  • Properties of angles:

    • When two rays emerge from a common point it is called a vertex of angles.

    • The two rays forming the angle are called their sides or arms.

    • A reflex angle is formed when an angle is less than 360 degrees and greater than  180 degrees. 

    • When two adjacent angles meet at 180 degrees is called a pair of angles. 

    • Vertically opposite pairs of angles are formed when two lines intersect each other. 

1. Fill in the blanks:

     (i) If two angles are complementary, then the sum of two angles is equal to  _______.

     (ii) If two angles are supplementary, then the sum of two angles is equal to ______.

     (iii) Two angles forming a linear pair are _______________.

     (iv) If two adjacent angles are supplementary, they form a ___________.

     (v) If two lines intersect at a point, then the vertically opposite angles are always                                  

______.

Solution: (i) 90o

                 (ii) 180o

                 (iii) supplementary angles  

                 (v)  linear pair

                (iv) equal

      2.  Find the complementary angles of the given figure:

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Image 1

Solution: The sum of two angles equal to 90 degrees is said to be complementary angles. 

          The given angle is 20 degrees. Let the measure of its complementary angle be y degree. 

            = y + 20o = 90o

            = y = 90o – 20o

            = y = 70o

          Hence, the complementary angle is equal to 70o.

      3. Find the supplementary angle of the given figure:

 

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Image 4

Solution:- The sum of two angles is equal to 180 degrees is said to be complementary angles.

                       The given angle is 105o

                       Let the measure of its supplement be xo.

                      Then,

                      = x + 105o = 180o

                      = x = 180o – 105o

                      = x = 75o

                      Hence, the supplementary angle is equal to 75o.

       4. In the following figure, is ∠1 adjacent to ∠2? Give reasons.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Image 10

Solution:-

∠1 and ∠2 are not adjacent angles. Because they are not lying on the same vertex.

 

1. What are the five types of Related Angles?

The five types of related angles are:

    • Complementary angles

    • Supplementary angles

    • Adjacent angles

    • Linear pair angles

    • Vertically opposite angles

2. What are the properties of Lines and Angles?

If two parallel lines are intersected by a transversal then:

    • Its vertically opposite angles are always equal

    • Its corresponding angles are equal

    • Its alternate exterior and interior angles are equal

 3. What are Lines and their types?

Lines are straight, one-dimensional figures that extend in the opposite direction of their origin infinitely. A line can be horizontal or vertical, and drawn from left to right or top to bottom. The lines are of many types such as:

    1. Horizontal lines

    2. Vertical lines

    3. Parallel lines

    4. Perpendicular lines

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