NCERT Solutions for Class 9 Maths Chapter 6 : Lines and Angles

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The NCERT Solutions for Class 9 Maths have been provided in this article. Lines are dots spaced together that extend infnitely in two directions. Angles are shapes that form once two rays meet at the endpoint.

Class 9 Maths Chapter 6 Lines and Angles belong to Unit 4 Geometry which has a weightage of 27 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 6 cover the following important concepts:

Angle Sum Property of a Triangle
Lines and Angles
Parallel Lines and a Transversal

Download: NCERT Solutions for Class 9 Mathematics Chapter 6 pdf

NCERT Solutions for Class 9 Mathematics Chapter 6

The Chapter 6 Class 9 Maths are given below:

Important Topics in Class 9 Maths Chapter 6 Lines and Angles

Important Topics in Class 9 Maths Chapter 6 Lines and Angles are elaborated below:

Angle Sum Property of a Triangle

Angle sum property of a triangle claims that the sum of interior angles of a triangle is 180°. It is used to determine the measure of an unknown interior angle when the values of the other angles are known.

Angle Sum Property of a Triangle can be expressed by the following formula:
S = ( n − 2) × 180°

Lines and Angles

A line is a straight one-dimensional shape that extends infinitely in two directions. Angles form when two lines intersect one another. It can be represented by the symbol ∠.

Example: List what happens when two parallel lines are intersected by a transversal?

Solution: Assuming that two parallel lines are intersected by a transversal, the following occurs:

The vertically opposite angles are equal.
The corresponding angles are equal as well.
The alternate exterior and interior angles are equal too.

Parallel Lines and a Transversal

Parallel lines always remain the same distance apart and actually never meet. While, a transversal is any line that intersects two or more lines.

Example: What are some properties of a Transversal?

Solution: Some properties of a transversal are:

Its corresponding angles are always equal.
Its vertically opposite angles are found equal.
Its alternate interior angles are equal too.
Its alternate exterior angles are equal too.

NCERT Solutions for Class 9 Maths Chapter 6 Exercises:

The detailed solutions for all the NCERT Solutions for Lines and Angles under different exercises are:

Also check:

Chapter Related Topics
Pairs of Angles	Parallel Lines and a Transversal	Collinear Points
Vertex	Linear Pair Axiom	Transversal
Corresponding Angles Axiom	Alternate Angles	Properties of Parallel Lines
Angle Formula	Obtuse Angle	Class 9 Maths Chapter 6 Lines and Angles MCQs
Adjacent Angles Vertical	Linear Pair of Angles	Intersecting Lines and Non Intersecting Lines

Also Read:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

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2.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not

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3.
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

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4.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

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5.
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
Length (in mm)
Number of leaves
118 - 126
3
127 - 135
5
136 - 144
9
145 - 153
12
154 - 162
5
163 - 171
4
172 - 180
2
Find the median length of the leaves.
(Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

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6.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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NCERT Solutions for Class 9 Maths Chapter 6 : Lines and Angles