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NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers

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NCERT Solutions for Class 6 Chapter 2 Maths FREE PDF Download

Class 6 Maths Chapter 2, Lines and Angles, students are introduced to fundamental concepts about lines, rays, and angles. Chapter 6 lays the groundwork for understanding more complex geometrical concepts in higher grades. Through this chapter, students explore the different types of lines and angles and their properties, along with practical applications. Mastering these basics is crucial for solving geometrical problems accurately. The chapter helps build a solid understanding of geometry, which is essential for future mathematical studies.

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Table of Content
1. NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers - FREE PDF Download
2. Glance on Maths Chapter 2 Class 6 - Whole Numbers
3. Access NCERT Solutions for Maths Chapter 2 – Whole Numbers
4. NCERT Solutions for Class 6 Maths Chapter 2 PDF
    4.12.1 Introduction
    4.22.2 Whole Numbers
    4.32.3 Number Line
5. Overview of Deleted Syllabus for CBSE Class 6 Maths Whole Numbers
6. Class 6 Maths Chapter 2: Exercises Breakdown
7. Other Study Material for CBSE Class 6 Maths Chapter 2
8. Chapter-Specific NCERT Solutions for Class 6 Maths
FAQs


Our Class 6 Maths NCERT Solutions PDF breaks the lesson into easy-to-understand explanations, making learning fun and interactive. Students will develop essential language skills with engaging activities and exercises. Check out the revised CBSE Class 6 Maths  Syllabus and start practising Maths Class 6 Chapter 2.


Glance on Class 6 Maths  Lines and Angles Chapter 2

  • Point, Line, Line Segment, and Ray: Understanding the basic geometric entities and their properties.

  • Intersecting and Parallel Lines: Introduction to lines that meet at a point and those that never meet.

  • Types of Angles: Definitions and properties of acute, obtuse, right, straight, and reflex angles.

  • Measuring Angles: Use of protractors to measure angles accurately.

  • Complementary and Supplementary Angles: Learning how two angles can form 90° and 180°, respectively.

  • Vertically Opposite Angles: Understanding how intersecting lines create equal angles.

  • Linear Pair: Exploring the relationship between adjacent angles on a straight line

Access NCERT Solutions for Class 6 Maths Chapter 2

2.4 Ray Figure it Out (Page No. 15-17)

Question 1.


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Can you help Rihan and Sheetal find their answers?
Answer: Infinite number of lines can be drawn to pass through a point in a plane.
One and only one line can be drawn to pass through two points.


Question 2. Name the line segments in Fig. below. Which of the five marked points are on exactly one of the line segments? Which are on two of the line segments?


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Answer:
Line segments: LM, MP, PQ and QR
Points L and R are on one line segment only. Points M, P and Q are on two line segments. 


Question 3. Name the rays shown in Fig. below. Is T the starting point of each of these rays?


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Answer

Ray \(\overline{\mathrm{TA}}\) and ray \(\overline{\mathrm{TB}}\) (can be also called ray TN). Yes, T is the starting point of each of the 2 rays, \(\overline{\mathrm{TA}}\) and \(\overline{\mathrm{TB}}\).


Question 4. Draw a rough figure and write labels appropriately to illustrate each of the following:
(a) \(\overline{\mathrm{OP}}\) and \(\overline{\mathrm{OQ}}\) meet at O.
Answer:


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(b) \(\overline{\mathrm{XY}}\) and \(\overline{\mathrm{PQ}}\) intersect at point M.
Answer:


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(c) Line l contains points E and F but not point D.
Answer:


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(d) Point P lies on AB.
Answer:


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Question 5. In Fig. below name:


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(a) Five points
(b) Aline
(c) Four rays
(d) Five line segments
Answer:
Points B, C, D, E and O.
Line: DB
Rays: \(\overrightarrow{\mathrm{OB}}, \overrightarrow{\mathrm{OC}}, \overrightarrow{\mathrm{OD}} ; \overrightarrow{\mathrm{OE}}\)
Line segments: DE, EO, OB, DC, DO.


Question 6. Here is a ray \(\overrightarrow{\mathrm{OB}}\) (Fig.). It starts at O and passes through the point A. It also passes through the point B.
(a) Can you also name it as \(\overrightarrow{\mathrm{OB}}\)? Why?
(b) Can we write \(\overrightarrow{\mathrm{OA}}\) as \(\overrightarrow{\mathrm{AO}}\) ? Why or why not?
Answer:
(a) Yes, Ray \(\overrightarrow{\mathrm{OA}}\) can also be named as ray \(\overrightarrow{\mathrm{OB}}\) as initial point and direction remains same.
(b) Ray \(\overrightarrow{\mathrm{OA}}\) cannot be named as ray \(\overrightarrow{\mathrm{AO}}\) as the initial point of the ray is O, not A.


2.5 Angle Figure it Out (Page No. 19-21)

Question 1. Can you find the angles in the given pictures? Draw the rays forming any one of the angles and name the vertex of the angle.


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Answer:
(a) ∠ADB, ∠BDC, vertex: D
(b) ∠PQR, vertex: Q


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(c) ∠LMN, vertex: M


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(d) ∠XYZ, vertex: Y


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Question 2. Draw and label an angle with arms ST and SR.
Answer:


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Question 3. Explain why ∠APC cannot be labelled as ∠P.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 13


Answer:
Sol. At P there are three angles.
∠P could mean ∠APB or ∠BPC or ∠APC.
To get the correct angle, it has to be named as ∠APC or ∠APB or ∠BPC.
Also note that a single point can not form an angle.


Question 4. Name the angles marked in the given figure.


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Answer:
Angles in the figure are :
Angle 1 is ∠RTP
Angle 2 is ∠RTQ


Question 5. Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C? Write them down, and mark each of them with a curve as in Fig. (SeeNCERT Textbook,page 18).
Answer:


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We get three lines.
These are line AB, line BC and line CA.
Also, we get three angles.
These are ∠ABC, ∠BCA and ∠CAB.


Question 6. Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C, D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C, D? Write them all down, and mark each of them with a curve as in Fig. (See NCERT Textbook, page 18).
Answer:


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We get six lines.
These are line AB, line BC, line CD, line DA, line AC and line BD.
Also, we get twelve angles.
These are ∠BAC; ∠CAD, ∠BAD, ∠ABD, ∠DBC, ∠ABC, ∠BCA, ∠ACD, ∠BCD, ∠CDB, ∠CDA, ∠BDA.


2.6 Comparing Angles Figure it Out (Page No. 23)

Question 1. Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the angles formed between the fold and the sides of the paper. Make different angles by folding a rectangular sheet of paper and compare the angles. Which is the largest and smallest angle you made?


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 17


Answer:
Let’s mark the rectangle and vertex of the fold as shown in figure below.


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We get ∠1, ∠2, ∠3 and ∠4.
Comparing: ∠1 < ∠2, ∠4 < ∠3,
∠1 = ∠4, ∠2 = ∠3.
∠2 and ∠3 are the largest angles.
∠1 and ∠4 are the smallest angles.


Question 2. In each case, determine which angle- is greater and why.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 19


(a) ∠AOB or ∠XOY
(b) ∠AOB or ∠XOB
(c) ∠XOB or ∠XOC
Discuss with your friends on how you decided which one is greater.
Answer:
(a) ∠AOB > ∠XOY
(∠AOB has more spread than ∠XOY)

(b) ∠AOB > ∠XOB
(∠AOB has more spread than ∠XOB)

(c) ∠XOB = ∠XOC
(B and C are points on same ray; both angles have same arms and vertex, hence same spread)


Question 3. Which angle is greater: ∠XOY or ∠AOB? Give reasons.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 20


Answer:


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∠1 > ∠3
(∠1 has more spread than ∠3)
∠1 + ∠2 > ∠3 + ∠2
(adding ∠2 to both sides)
Hence, ∠XOY > ∠AOB


2.7 Making Rotating Arms 2.8 Special Types of Angles Figure it Out (Page No. 29-31)

Question 1. How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?
Answer: A window has 4 right angles.
∠1, ∠2, ∠3 and ∠4.
Yes. At comers of door. At comers of blackboard etc.


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Question 2. Join A to other grid points in the figure by a straight line to get a straight angle. What are all the different ways of doing it?


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 23


Answer:


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This can be done in one way.


Question 3. Now join A to dther grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it?


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 25


Hint: Extend the line further as shown in the figure below. To get a right angle at A, we need to draw a line through it that divides the straight angle CAB into two equal parts.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 26


Answer:


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Question 4. Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease.
(a) How many right angles do you have now? Justify why the angles are exact right angles.
Answer

We get four right angles.
Let P be the point of intersection of the two creases.
The two creases are perpendicular lines meeting at P.
Hence, all four angles are right angles.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 28


(b) Describe how you folded the paper so that any other person who doesn’t know the process can simply follow your description to get the right angle.
Answer:


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Step 1. Take a sheet of paper and fold it. Step 2. Crease the fold.
Step 3. Now again fold the paper so that the two parts of the crease coincide.
Step 4. Crease the fold.
Step 5. Unfold both the creases.
We get two perpendicular lines and four right angles as shown above.


2.7 Making Rotating Arms 2.8 Special Types of Angles Figure it Out (Page No. 31-32)

Question 1. Identify acute, right, obtuse and straight angles in the given figures (See NCERT TB, Page 31).
Answer:


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Question 2. Make a few acute angles and a few obtuse angles. Draw them in different orientations.
Answer:


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Question 3. Do you know what the words acute and obtuse mean? Acute means sharp and obtuse means blunt. Why do you think these words have been chosen?
Answer:
Word ‘acute’ means ‘sharp’. The vertex of the angle appears as a sharp tip.
Word ‘obtuse’ means ‘blunt’. The vertex of the angle appears as a blunt tip.


Question 4. Find out the number of acute angles in each of the figures below.


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What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?
Answer:


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3 + 9=12
12 + 9 = 21
In every step, the numbers of angles increases by 9.

Next figure will be as follows:


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Number of acute angles = 21 + 9 = 30


2.9 Measuring Angles Figure it Out (Page No. 35)

Question 1. Write the measures of the following angles:


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(a) ∠KAL
Notice that the vertex of this angle coincides with the centre of the protractor. So the number of units of 1 degree angle between KA and AL gives the measure of ∠KAL. By counting, we get ∠KAL = 30°.
Making use of the medium sized and large sized marks, is it possible to count the number of units in 5s or 10s?
(b) ∠WAL
(c) ∠TAK
Answer:
(a) ∠KAL = 30°
(b) ∠WAL = 50°
(c) ∠TAK = 120°


2.9 Measuring Angles Figure it Out (Page No. 40-43)

Question 1. Find the degree measures of the following angles using your protractor.


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Answer:
(a) ∠IHJ = 47°
(b) ∠IHJ = 24°
(c) ∠IHJ =110°


Question 2. Find the degree measures of different angles in your classroom using your protractor. .
Answer:
Angle at comer of blackboard = 90°
Angle at comer of desk = 90°


Question 3. Find the degree measures for the angles given below. Check if your paper protractor can be used here!


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Answer:
(a) ∠IHJ = 42°
(b) ∠IHJ =116°
Paper protractor cannot be used here.


Question 4. How can you find the degree measure of the angle given below using a protractor?


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Answer:
We require measure of reflex ∠AOB.
Step 1. We find measure of ∠AOB.
Step 2. We find 360° ∠AOB.
This is the required measure.


Question 5. Measure and write the degree measures for each of the following angles:


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Answer:
(a) Measure of given angle is 80°
(b) Measure of given angle is 120°
(c) Measure of given angle is 60°
(d) Measure of given angle is 130°
(e) Measure of given angle is 130°
(f) Measure of given angle is 60°


Question 6. Find the degree measures of ∠BXE, ∠CXE, ∠AXB and ∠BXC.


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Answer:
(a) ∠BXE =115°
(b) ∠CXE = 85°
(c) ∠AXB = 65°
(d) ∠BXC = 30°


Question 7. Find the degree measures of ∠PQR, ∠PQS and ∠PQT.


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Answer:
(a) ∠PQR = 45°
(b) ∠PQS = 105°
(c) ∠PQT = 150°


Question 8. Make the paper craft as per the given instructions. Then, unfold and open the paper fully. Draw lines on the creases made and measure the angles formed.


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Answer: Do it yourself.


Question 9. Measure all three angles of the triangle shown in Fig. (a), and write the measures down near the respective angles. Now add up the three measures. What do you get? Do the same for the triangles in Fig. (b) and (c). Try it for other triangles as well, and then make a conjecture for what happens in general! We will come back to why this happens in a later year.


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Answer:
∠A + ∠B + ∠C = 180°


2.9 Measuring Angles Figure it Out (Page No. 45-46)

Question 1. Angles in a clock:
(a) The hands of a clock make different angles at different times. At 1 o’clock, the angle between the hands is 30°. Why?
(b) What will be the angle at 2 o’clock? And at 4 o’clock? 6 o’clock?
(c) Explore other angles made by the hands of a clock.


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 44


Answer:
(a) Numbers 1 to 12 are written along the circumference of a clock at equal distances.
360 ÷ 12 = 30.
Hence, angle between two consecutive numbers is 30°
At 1°’ clock hands are at 0 and 1 (consecutive numbers)
Hence angle between them is 30°.

(b) Angle between hands at 2 o’ clock = 2 × 30° = 60° angle between hands at 4 o’clock = 4 × 30°= 120°
Angle between hands at 6 o’ clock = 6 × 30°= 180°

(c) Angle between hands at 5 o’ clock = 5 × 30°= 150°
Angle between hands at 7 o’ clock = 7 × 30° = 210°
Angle between hands at 8 o’ clock = 8 × 30° = 240°


Question 2. The angle of a door: Is it possible to express the amount by which a door is opened using an angle? What will be the vertex of the angle and what will be the arms of the angle?


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Answer: Yes, it is possible.


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Here, vertex is B, and arms are AB and BC.


Question 3. Vidya is enjoying her time on the swing. She notices that the greater the angle with which she starts the swinging, the greater is the speed she achieves on her swing. But where is the angle? Are you able to see any angle?


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Answer: Yes, an angle can be seen.


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Question 4. Here is a toy with slanting slabs attached to its sides; the greater the angles or slopes of the slabs, the faster the balls roll. Can angles be used to describe the slopes of the slabs?


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Answer: Greater the angle, greater the slope.
For each angle one arm is a side and one arm is the slope.


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Question 5. Observe the images below where there is an insect and its rotated version, fan angles be used to describe the amount of rotation? How? What will be the arms of the angle and the vertex?
Hint: Observe the horizontal line touching the insects.


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Answer: Both insects are rotated 90° clockwise.


2.10 Drawing Angles Figure it Out (Page No. 49-50)

Question 1. In Fig. below, list all the angles possible. Did you find them all? Now, guess the measures of all the angles. Then, measure the angles with a protractor. Record all your numbers in a table. See how close your guesses are to the actual measures.


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Answer: The given figure has 20 angles.
Guess: ∠1 = ∠4 = 60°; ∠2 = ∠3 = 120° by actual measure: ∠1 = ∠4 = 70°; ∠2 = ∠3 = 110°.


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Question 2. Use a protractor to draw angles having the following degree measures:
(a)110°
(b) 40°
(c) 75°
(d)1120
(e) 134°
Answer:


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Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 55


Question 3. Draw an angle whose degree measure is the same as the angle given below:


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Also, write down the steps you followed to draw the angle.
Answer:
Step 1. Measure the given angle (∠IHJ = 120°)
Step 2. Using a protractor draw ∠ABC = 120°


2.11 Types of Angles and their Measures Figure it Out (Page No. 51-52)

Question 1. In each of the below grids, join A to other grid points in the figure by a straight line lo get:
(a) An acute Angle


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(b) An obtuse Angle


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(c) A reflex Angle


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Mark the intended angles with curves to specify the angles. One has been done for you.
Answer:


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Question 2. Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or reflex.
a. ∠PTR
b. ∠PTQ
c. ∠PTW
d. ∠WTP


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Answer:
(a) ∠PTR = 300 acute
(b) ∠PTQ = 60° acute
(c) ∠PTW = 105° obtuse
(d) ∠WTP = 225° reflex


2.11 Types of Angles and their Measures Figure it Out (Page No. 53-54)

Question 1. Draw angles with the following degree measures:
(a) 140°
(b) 82°
(c) 195°
(d) 70°
(e) 35°
Answer:


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Question 2. Estimate the size of each angle and then measure it with a protractor:


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Classify these angles as acute, right, obtuse or reflex angles.
Answer:
(a) 45° acute
(b) 150° obtuse
(c) 120° obtuse
(d) 30° acute
(e) 95° obtuse
(f) 350° reflex


Question 3. Make any figure with three acute angles, one right angle and two obtuse angles.
Answer:


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Angles 1, 2 and 3 are acute angles, angle 4 is right angle, angles 5 and 6 are obtuse angles.


Question 4. Draw the letter ‘M’such that the angles on the sides are 40° each and the angle in the middle is 60°.
Answer:


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∠1 = 30°, ∠2 = 30°, ∠3 = 60°


Question 5.cDraw the letter ‘Y’ such that the three angles formed are 150°, 60° and 150°.
Answer:


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∠1 = 150°, ∠2 = 60°, ∠3 = 150°


Question 6. The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? What is the largest acute angle formed between two spokes?


Lines and Angles Class 6 NCERT Solutions Ganita Prakash Maths Chapter 2 67


Answer: Angle between two consecutive spokes = 360 ÷ 24 = 15°
Largest acute angle = 5 × 15° = 75°


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Question 7. Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure?
Answer: Let the measure of the angle be m
Then 5 × m > 90 but 4 × m < 90
or m > \(\frac{90}{5}\) and m < \(\frac{90}{4}\)
Hence m > 18 but m < 22 ½
Hence measure of the angle is 19° or 20° or 21°


Benefits of NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles

  1. Draw different types of lines and angles to better understand them.

  2. Get comfortable with measuring angles using a protractor.

  3. Understand and remember key terms like point, line, ray, and the different types of angles.

  4. Work through NCERT problems and examples to strengthen your grasp of the concepts.

  5. Relate the concepts to everyday objects, such as a ladder against a wall (right angle) or scissors (intersecting lines).

  6. Keep revisiting the chapter's key points and practice questions to retain the information.


Important Study Material Links for Maths Chapter 2 Class 6 

S.No.

Important Study Material Links for Chapter 2

1.

Class 6 Lines and Angles Important Questions

2.

Class 6 Lines and Angles Notes



Conclusion

Chapter 2 of Class 6 Maths, Lines and Angles, provides students with the foundational knowledge of geometry. By learning to identify and measure different lines and angles, students build a base for more advanced topics in mathematics. Consistent practice and understanding of the basic concepts will not only help in excelling in this chapter but also prepare students for future mathematical challenges.


Chapter-wise NCERT Solutions Class 6 Science

After familiarising yourself with the Class 6 Maths  Chapter 2 Question Answers, you can access comprehensive NCERT Solutions from all Class 6 Maths textbook chapters.


S.No

Chapterwise Links for Class 6 Maths NCERT Solutions 

1

Chapter 1 Patterns In Mathematics Solutions 

3

Chapter 3 Number Play Solutions 

4

Chapter 4 Data Handling and Presentation Solutions 

5

Chapter 5 Prime Time Solutions 

6

Chapter 6 Perimeter and Area Solutions 

7

Chapter 7 Fractions Solutions 

8

Chapter 8 Playing with Constructions Solutions 

9

Chapter 9 Symmetry Solutions 

10

Chapter 10 The Other Side of Zero Solutions 



Related Important Links for Class 6  Maths

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6-


FAQs on NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers

1. Explain the Closure Property on Addition and Multiplication with an example.

The closure property of addition and multiplication states that when you add or multiply any two numbers from a set, the result will also be a number from the same set.


For example, if you add two whole numbers, the result will always be a whole number. Similarly, if you multiply two whole numbers, the result will always be a whole number.

For addition, a + b = b + a

3000 + 5000 = 8000

5000 + 3000 = 8000

For multiplication,  a x b = b x a

25 x 50 = 1250

50 x 25 = 1250 

2. Explain the Associative Property on Addition and Multiplication with an example.

The Whole Numbers can satisfy the associated property on both additions and multiplications similar to the closure property. Let's see an example of this.

For addition, a+(b+c) = (a+b)+c

 2+ (4+6) = (2+4)+6 = 12

For multiplication, a x (b x c )= (a x b) x c

2 x (4 x 6) = (2 x 4) x 6 = 48

3. What are the properties available in Mathematics for numbers?

Generally, we have six properties for the numbers. However, there will not be any compulsion that all members should satisfy all the properties. Some of the properties were satisfied and some may not. The basic properties available are -

  • Closure property

  • Associative property

  • Commutative property

  • Distributive property

  • Identity property

  • Inverse property etc.

4. Where can I access the solutions for Class 6 Maths Chapter 2?

Class 6 Chapter 2 is an easy chapter if practised regularly. To make it easier, you can easily avail the solutions on Vedantu. The solutions can easily be accessed free of cost via the link given. There are a variety of modules and example papers available on the Vedantu website and the Vedantu mobile app for those who are interested and want to do well in their exams. 

5. What is the whole number in Class 6 Maths Chapter 2?

Whole numbers are basic counting numbers in mathematics: 0, 1, 2, 3, 4,... These include 55, 88, 69856555 etc. Natural numbers beginning with 1 are included in the definition of whole numbers. Positive integers and 0 are included in whole numbers. For more information and guidance you can visit the Vedantu Site (vedantu.com) or the Vedantu app. The problems of this chapter can be tricky sometimes and hence it is advisable to practice them carefully even if you find them simple. Practice well for your exams!

6. Do I need to practice all the questions provided in Class 6 Maths Chapter 2 NCERT Solutions?

Indeed. It is very important that you practice and answer all questions since they cover a variety of subjects and concepts and will give you a good understanding of the kind of questions that might be set from those areas and the framework of the question paper. These questions also help you learn how different questions from the same topic may be set. Each exercise should be thoroughly revised. The Vedantu website and Vedantu mobile app both provide a variety of modules as well as example papers on these subjects if you're so inclined.

7. What is the number 0?

Zero is a number that can be classified as a whole number, a real number, and a non-negative integer. It is not classified as undercounting, odd, positive natural or negative whole numbers and neither a complex number. It is quite tricky to classify zero into different categories. It can be included in multiple equations involving complex numbers though. Practice all the problems related to these topics and other topics of this chapter as well in order to score well in them.

8. Can zero be classified as a natural number?

Zero is a number that is a whole number, a real number, and a non-negative integer. It is neither a counting, odd, positive natural, or negative whole number, nor is it a complex number. It is difficult to categorise zero in numerous ways. It can, however, be used in numerous equations involving complex values.  If you are interested in obtaining various modules and example papers relating to these areas, you can simply get them through the Vedantu website as well as the Vedantu mobile app.