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# NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles

NCERT Solutions for Class 7 Maths Chapter 5 is a sample chapter on the geometrical concept of Lines and Angles. In this chapter, there are only 2 exercises and a total of 20 questions. We will study Related Angles and Pairs of Lines. We will also learn to check parallel lines.

Try these NCERT Solutions for class 7 chapter 5 ‘Lines and Angles’ which are based on the latest CBSE approved syllabus. You can consider them as the most reliable study material for Class 7 Maths. We, at Instasolv, provide Chapter-wise Solutions of NCERT Class 7 Maths Book. These answers will help you in understanding the concepts of each Chapter and improve your speed of solving any question of any type based on these concepts.

For the Maths subject in Class 7, we follow an approach where we explain the important elements and summarise each part and subpart of the Chapter- Lines and Angles. We will follow the same sequence as in the book so that it becomes easy to refer and understand. Lines and Angles Class 7 notes will help you strengthen your concepts and help you in scoring higher marks in the exams.

## NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles: Exercise Discussion

As discussed above, there are only 2 exercises present in this chapter. The questions in each of the exercises is based on the following topics:

1. Introduction – This is a refreshment of the concept of a line segment, line, and ray and the way they are denoted.

A line segment has two endpoints.

A line segment whose endpoints are extended endlessly in either direction becomes a line. So a line has no endpoint.

A ray has one endpoint.

The direction in which the segment extends endlessly is shown by an arrow.

When lines or line segments meet an arrow is formed.

2. Related Angles

• Complementary Angles

When the sum of the measures of two angles is equal to ninety degrees, the two angles are called complementary angles. Each of these two complementary angles is called the complement of the other.

This also proves that only two acute angles where the measure of each of them is less than ninety degrees can form complementary angles.

• Supplementary Angles

When the sum of the measures of two angles is equal to one hundred and eighty degrees, the two angles are called supplementary angles. Each of these two supplementary angles is called as the supplement of the other.

This also proves that any two acute angles where the measure of each of them is less than ninety degrees can not form supplementary angles. Either there has to be two right angles each of which measures ninety degrees or there has to be one obtuse angle and one acute angle. Two obtuse angles where each of them measures more than ninety degrees also cannot form supplementary angles because the total of the measure of two obtuse angles would be greater than one hundred and eighty degrees.

Angles that have a common arm and vertex but no interior common area are called adjacent angles.

Adjacent angles can be complementary or supplementary angles.

• Linear Pair

A linear pair is one type of adjacent angles. When the non-common sides of adjacent angles are opposite rays these adjacent angles form a linear pair.

• Vertically Opposite Angles

When two lines intersect, two pairs of vertically opposite angles are formed. These vertically opposite angles are equal in measure.

3. Pair of Lines

• Intersecting Lines

Two lines can only intersect at one point.

• Transversal

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

• Angles Made by a Transversal

Consider that the transversal is intersecting two lines at distinct points. At each intersecting point, four angles will be formed totaling 8 angles.

There will be four angles that lie in between the two lines that were intersected by the transversal. These are called interior angles.

– The other four angles are called exterior angles.

– There will be two pairs of interior angles on the same side of the transversal

– The pair of interior angles, one on each side of the transversal are called alternate angles. There will be two such pairs of alternate interior angles.

– Similarly, there will be two pairs of alternate exterior angles and two pairs of exterior angles on the same side of the transversal.

• Transversal of Parallel Lines

This is an important transversal which has many practical applications like a ladder. Properties of the transversal of Parallel Lines are:

– Each pair of corresponding angles are equal in measure

– Each pair of alternate interior angles are equal in measure

– Each pair of interior angles on the same side of the transversal are supplementary

• Checking of Parallel Lines

The same properties of the transversal of parallel lines can be used to check whether two lines are parallel

– When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.

When a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel.

When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel

Study Tips for NCERT Class 7 Maths  Chapter 5: Lines and Angles

Every student aims to get a high score in the exams. Instasolv recommends that you first read this chapter of CBSE NCERT textbook for Class 7 Maths.

Instasolv has provided a simple explanation and summary for each part and subpart of Chapter 5, Lines and Angles. Use this to develop a better understanding of all the concepts.

Thereafter, the suggested steps are:

a. If any concept is still not understood, ask the experts on the Instasolv app.

b. Do all the exercises, solved examples and self-practice questions on your own.