NCERT Solutions for Exercise 6.1 Class 9 Maths Chapter 6 - Lines and Angles

# NCERT Solutions for Exercise 6.1 Class 9 Maths Chapter 6 - Lines and Angles

Edited By Safeer PP | Updated on Jul 18, 2022 02:16 PM IST

A line with two endpoints is referred to as a line segment, and a portion of a line with one endpoint is referred to as a ray.

Collinear points are those that have three or more points on the same line; otherwise, they are non-collinear points. When two rays originate from the same endpoint, an angle is formed.

The rays that form an angle are referred to as the angle's arms, and the endpoint is referred to as the vertex of the angle.

NCERT Solutions Class 9 Maths exercise 6.1 – In NCERT solutions for Class 9 Maths chapter 6 exercise 6.1 we get to know that an acute angle has a range of 0° to 90°, whereas a right angle has a value of 90°. An obtuse angle is one that is greater than 90° but less than 180°.

Also, keep in mind that a straight angle equals 180°. A reflex angle is an angle that is greater than 180° but less than 360°. Furthermore, two angles with a sum of 90° are referred to as complementary angles, while two angles with a sum of 180° are referred to as supplementary angles.

Along with Class 9 Maths, chapter 8 exercise 6.1 the following exercises are also present.

## Lines and Angles Class 9 Maths Chapter 6 Exercise: 6.1

Given that,
AB is a straight line. Lines AB and CD intersect at O. $\angle AOC + \angle BOE = 70^0$ and $\angle$ BOD = $40^0$
Since AB is a straight line
$\therefore$ $\angle$ AOC + $\angle$ COE + $\angle$ EOB = $180^0$
$\Rightarrow \angle COE = 180^0-70^0=110^0$ [since $\angle AOC + \angle BOE = 70^0$ ]

So, reflex $\angle$ COE = $360^0-110^0 = 250^0$
It is given that AB and CD intersect at O
Therefore, $\angle$ AOC = $\angle$ BOD [vertically opposite angle]
$\Rightarrow \angle COA = 40^0$ [ GIven $\angle$ BOD = $40^0$ ]
Also, $\angle AOC + \angle BOE = 70^0$
So, $\angle$ BOE = $30^0$

Given that,
Line XY and MN intersect at O and $\angle$ POY = $90^0$ also $a:b = 2:3 \Rightarrow b = \frac{3a}{2}$ ..............(i)

Since XY is a straight line
Therefore, $\\a+b+\angle POY = 180^0\\ a+b = 180^0-90^0 = 90^0$ ...........(ii)
Thus, from eq (i) and eq (ii), we get
$\\\Rightarrow \frac{3a}{2}+a = 90^0\\$
$\\\Rightarrow a = 36^0\\$
So, $b = 54^0\\$
Since $\angle$ MOY = $\angle$ c [vertically opposite angles]
$\angle$ a + $\angle$ POY = c
$126^0 =c$

Given that,
ABC is a triangle such that $\angle$ PQR = $\angle$ PRQ and ST is a straight line.
Now, $\angle$ PQR + $\angle$ PQS = $180^0$ {Linear pair}............(i)
Similarly, $\angle$ PRQ + $\angle$ PRT = $180^0$ ..................(ii)

equating the eq (i) and eq (ii), we get

$\angle PQR +\angle PQS =\angle PRT + \angle PRQ$ {but $\angle$ PQR = $\angle$ PRQ }
Therefore, $\angle$ PQS = $\angle$ PRT
Hence proved.

Given that,
$x+y = z+w$ ..............(i)
It is known that, the sum of all the angles at a point = $360^0$
$\therefore$ $x+y+z+w=360^0$ ..............(ii)

From eq (i) and eq (ii), we get

$\\2(x+y)=360^0\\ x+y = 180^0$

Hence proved AOB is a line.

Given that,
POQ is a line, OR $\perp$ PQ and $\angle$ ROQ is a right angle.
Now, $\angle$ POS + $\angle$ ROS + $\angle$ ROQ = $180^0$ [since POQ is a straight line]
$\\\Rightarrow \angle POS + \angle ROS = 90^0\\ \Rightarrow \angle ROS = 90^0-\angle POS$ .............(i)
and, $\angle$ ROS + $\angle$ ROQ = $\angle$ QOS
$\angle ROS = \angle QOS -90^0$ ..............(ii)

Add the eq (i ) and eq (ii), we get

$\angle \textup{ROS} = \frac{1}{2}(\angle \textup{QOS} - \angle \textup{POS})$

hence proved.

Given that,
$\angle$ XYZ = $64^0$ and XY produced to point P and Ray YQ bisects $\angle$ ZYP $\Rightarrow \angle QYP = \angle ZYQ$
Now, XYP is a straight line
So, $\angle$ XYZ + $\angle$ ZYQ + $\angle$ QYP = $180^0$
$\Rightarrow 2(\angle QYP )=180^0 - 64^0 = 116^0$
$\Rightarrow (\angle QYP )= 58^0$

Thus reflex of $\angle$ QYP = $360^0- 58^0 = 302^0$

Since $\angle$ XYQ = $\angle$ XYZ + $\angle$ ZYQ [ $\because$ $\angle QYP = \angle ZYQ$

$\angle XYQ$ = $64^0+58^0 = 122^0$

## More About NCERT Solutions for Class 9 Maths Exercise 6.1

In NCERT solutions for Class 9 Maths exercise 6.1, we get to know that if two angles share a common vertex, a common arm, and their non-common arms are on opposite sides of the common arm, they are adjacent.

A linear pair is formed when two adjacent angles are supplementary, i.e. they form a straight line (add up to 180).

When two lines intersect at a point, they form equal angles that are vertically opposite.

The sum of two adjacent angles formed by a ray on a line is 180°.

When the sum of two adjacent angles equals 180°, the angles' non-common arms form a line.

Also Read| Lines And Angles Class 9 Notes

## Benefits of NCERT Solutions for Class 9 Maths Exercise 6.1

• Exercise 6.1 Class 9 Maths, is based on the concepts of lines and angles

• From Class 9 Maths chapter 6 exercise 6.1 we learn about parallel lines and pairs of angles

• Understanding the concepts from Class 9 Maths chapter 6 exercise 6.1 will allow us to understand the concepts related to angle sum properties of LINES AND ANGLES.

Also see

## Subject Wise NCERT Exemplar Solutions

### Frequently Asked Question (FAQs)

1. What is the main concept of NCERT solutions for Class 9 Maths exercise 6.1?

This exercise is about lines and angles, types of angles like vertically opposite angles and axioms and concepts like parallel lines and pair of angles.

2. What is an angle?

An angle is a figure which is formed by two rays, called the sides of the angle, both of which shares a common endpoint, called the vertex of the angle.

3. What are collinear points?

If we have three or more points that lie on the same line then they are called collinear points.

4. Name the different types of angles?

There are various types of angles are:

• Acute angle

• Right angle

• Obtuse angle

• Straight angle

• Reflex angle

5. What do you understand by reflex angles?

A reflex angle is an angle greater than 180° and less than 360°.

6. What are intersecting lines?

When we have two or more lines meeting or crossing each other in a plane, they are termed as intersecting lines.

7. What is pair of angles?

When we have two lines sharing a common endpoint, called Vertex then an angle that is formed between these two lines is known as the pair of angles.

8. What do you understand by vertical opposite angles?

When we have two lines intersecting each other, the opposite angles are equal. These angles are known as the vertically opposite angles because they are equal and opposite to each other at the vertex.

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