NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles (PDF) – 2026-27

NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles provide clear, step-by-step answers to every exercise and in-text question from the chapter Lines and Angles of the NCERT textbook Ganita Prakash. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 6 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 6 Maths Chapter 2 question-answer PDF.

NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles

• Class: Class 6
• Subject: Maths
• Chapter: Chapter 2 – Lines and Angles
• Textbook: Ganita Prakash (NCERT)
• Study material: NCERT Solutions – questions with answers, free PDF

These solutions answer all the exercise questions of Chapter 2 Lines and Angles — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.

NCERT Solutions Class 6 Maths Chapter 2 Lines and Angles View Download

NCERT Solutions for Class 6 Maths Chapter 2 PDF Download

You can read the NCERT Solutions for Class 6 Maths Chapter 2 online above, or download the complete question-answer PDF to study Lines and Angles offline at any time.

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NCERT Solutions for Class 6 Maths Chapter 2 PDF Download Link – Click Here to Download Solutions PDF

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Questions Covered in This Chapter

These NCERT Solutions answer all 75 questions of this chapter. The questions solved are:

1. Mark any two points A and B on a sheet of paper. Try to connect A to B by various routes (Fig. 2.1). What is the shortest route from A to B?
2. Imagine that the line segment from A to B (i.e., AB) is extended beyond A in one direction and beyond B in the other direction without any end. This is a model for a line. Do you think you can draw a complete picture of a line? No. Why?
3. Rihan marked a point on a piece of paper. How many lines can he draw that pass through the point? Sheetal marked two points on a piece of paper. How many different lines can she draw that pass through both of the points? Can you help Rihan and Sheetal find their answers?
4. Name the line segments in Fig. 2.4. Which of the five marked points are on exactly one of the line segments? Which are on two of the line segments?
5. Name the rays shown in Fig. 2.5. Is T the starting point of each of these rays?
6. Draw a rough figure and write labels appropriately to illustrate each of the following: a. OP and OQ meet at O. b. XY and PQ intersect at point M. c. Line l contains points E and F but not point D. d. Point P lies on AB.
7. In Fig. 2.6, name: a. Five points b. A line c. Four rays d. Five line segments
8. Here is a ray OA (Fig. 2.7). It starts at O and passes through the point A. It also passes through the point B. a. Can you also name it as OB? Why? b. Can we write OA as AO? Why or why not?
9. Vidya has just opened her book. Let us observe her opening the cover of the book in different scenarios (Case 1 to Case 6). Do you see angles being made in each of these cases? Can you mark their arms and vertex?
10. Which angle is greater—the angle in Case 1 or the angle in Case 2?
11. In a compass or divider, we turn the arms to form an angle… A pair of scissors has two blades… Look at the pictures of spectacles, wallet and other common objects. Identify the angles in them by marking out their arms and vertices.
12. 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.
13. Draw and label an angle with arms ST and SR.
14. Explain why ∠APB cannot be labelled as ∠P.
15. Name the angles marked in the given figure.
16. 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. 2.9.
17. 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. 2.9.
18. Look at these animals opening their mouths. Do you see any angles here? If yes, mark the arms and vertex of each one. Can you arrange the angles in this picture from smallest to largest?
19. Is it always easy to compare two angles?
20. Here are some angles. Label each of the angles. How will you compare them? Draw a few more angles; label them and compare.
21. Where else do we use superimposition to compare?
22. 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?
23. In each case, determine which angle is greater and why. a. ∠AOB or ∠XOY b. ∠AOB or ∠XOB c. ∠XOB or ∠XOC. Discuss with your friends on how you decided which one is greater.
24. Which angle is greater: ∠XOY or ∠AOB? Give reasons.
25. Suppose we have a transparent circle which can be moved and placed on figures… Can you now tell which angle is bigger? Which crane was making the bigger angle?
26. Passing through a slit: Now, shuffle and mix up all the rotating arms. Can you identify which of the rotating arms will pass through the slit?
27. Challenge: Reduce this angle. (The arms are cut shorter — is the angle reduced?)
28. Let us consider a straight angle ∠AOB. Observe that any ray OC divides it into two angles, ∠AOC and ∠COB. Is it possible to draw OC such that the two angles are equal to each other in size? Justify why the two angles are equal.
29. If a straight angle is formed by half of a full turn, how much of a full turn will form a right angle?
30. Angles are classified in three groups as shown. Right angles are shown in the second group. What could be the common feature of the other two groups?
31. How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?
32. 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?
33. Now join A to other grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it? (Hint: Extend the line further. 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.)
34. 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. 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.
35. Identify acute, right, obtuse and straight angles in the previous figures.
36. Make a few acute angles and a few obtuse angles. Draw them in different orientations.
37. 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?
38. Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?
39. The circle has been divided into 1, 2, 3, 4, 5, 6, 8, 9, 10 and 12 parts below. What are the degree measures of the resulting angles? Write the degree measures down near the indicated angles.
40. Write the measures of the following angles: a. ∠KAL b. ∠WAL c. ∠TAK. (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?)
41. There are two sets of numbers on the protractor: one increasing from right to left and the other increasing from left to right. Why does it include two sets of numbers?
42. Name the different angles in the figure and write their measures. Did you include angles such as ∠TOQ? Which set of markings did you use — inner or outer?
43. What is the measure of ∠TOS? Can you use the numbers marked to find the angle without counting the number of markings? Here, OT and OS pass through the numbers 20 and 55 on the outer scale. How many units of 1 degree are contained between these two arms? Can subtraction be used here?
44. How can we measure angles directly without having to subtract? Place the protractor so the centre is on the vertex of the angle. Align the protractor so that one of the arms passes through the 0º mark. What is the degree measure of ∠AOB?
45. The measure of half a circle is ½ of a full turn. So, the measure of half a turn = ½ of ____ = 180°. The measure of a ¼ turn = ¼ of 360° = ________. When folded, this is ⅛ of the circle, or ⅛ of a turn, or ⅛ of 360°, or ¼ of 180° or ½ of 90° = ________. Continuing with another half fold, we get an angle of measure ________.
46. Think! In Fig. 2.19, we have ∠AOB = ∠BOC = ∠COD = ∠DOE = ∠EOF = ∠FOG = ∠GOH = ∠HOI = _____. Why?
47. Identify the angle bisectors in your handmade protractor. Try to make different angles using the concept of angle bisector through paper folding.
48. Find the degree measures of the following angles using your protractor.
49. Find the degree measures of different angles in your classroom using your protractor.
50. Find the degree measures for the angles given below. Check if your paper protractor can be used here!
51. How can you find the degree measure of the angle given below using a protractor?
52. Measure and write the degree measures for each of the following angles: a, b, c, d, e, f.
53. Find the degree measures of ∠BXE, ∠CXE, ∠AXB and ∠BXC.
54. Find the degree measures of ∠PQR, ∠PQS and ∠PQT.
55. 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.
56. Measure all three angles of the triangle shown in Fig. 2.21 (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. 2.21 (b) and (c). Try it for other triangles as well, and then make a conjecture for what happens in general!
57. A student used a protractor to measure the angles as shown (∠U = 35°, ∠V = 80°, ∠W = 70°, ∠X = 150°, ∠Y = 120°, ∠Z = 85°). In each figure, identify the incorrect usage(s) of the protractor and discuss how the reading could have been made and think how it can be corrected.
58. 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.
59. 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?
60. 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?
61. 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? What are the arms of each angle? Which arm is visible and which is not?
62. Observe the images below where there is an insect and its rotated version. Can 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.)
63. In Fig. 2.23, 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.
64. Use a protractor to draw angles having the following degree measures: a. 110° b. 40° c. 75° d. 112° e. 134°
65. Draw an angle whose degree measure is the same as the angle given below. Also, write down the steps you followed to draw the angle.
66. In each of the below grids, join A to other grid points in the figure by a straight line to get: a. An acute angle b. An obtuse angle c. A reflex angle. Mark the intended angles with curves to specify the angles. One has been done for you.
67. 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
68. In this figure, ∠TER = 80°. What is the measure of ∠BET? What is the measure of ∠SET? (Hint: Observe that ∠REB is a straight angle. Hence, the degree measure of ∠REB = 180° of which 80° is covered by ∠TER.)
69. Draw angles with the following degree measures: a. 140° b. 82° c. 195° d. 70° e. 35°
70. Estimate the size of each angle and then measure it with a protractor: a, b, c, d, e, f. Classify these angles as acute, right, obtuse or reflex angles.
71. Make any figure with three acute angles, one right angle and two obtuse angles.
72. Draw the letter 'M' such that the angles on the sides are 40° each and the angle in the middle is 60°.
73. Draw the letter 'Y' such that the three angles formed are 150°, 60° and 150°.
74. 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?
75. 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?

Chapter at a Glance

• A point shows an exact location. A line segment is the shortest path between two points, a line is a segment stretched endlessly both ways, and a ray starts at one point and goes on endlessly in one direction.
• Through one point you can draw endlessly many lines, but through two points only one line can be drawn.
• An angle is made by two rays with a common starting point. The common point is the vertex and the two rays are the arms . In ∠DBE the vertex is always the middle letter.
• The size of an angle is the amount of turn from one arm to the other — it does not depend on how long the arms are drawn.
• A full turn is divided into 360 equal parts ; each part is 1 degree (1°). So a straight angle is 180° and a right angle is 90°.
• Angles are named by their measure: acute (less than 90°), right (90°), obtuse (between 90° and 180°), straight (180°) and reflex (between 180° and 360°).

How to Download NCERT Solutions for Class 6 Maths Chapter 2 PDF

Follow these simple steps to get the Lines and Angles questions-and-answers PDF from Ganita Prakash.

1. Search NCERT Solutions for Class 6 Maths Chapter 2 aglasem and open this page.
2. Read the exercise questions with answers for Lines and Angles shown above.
3. Click the Download PDF link to save the Lines and Angles solutions to your device.

NCERT Solutions for Class 6 Maths – All Chapters

There are more chapters to study besides Lines and Angles in Maths. Here are the NCERT Solutions for all chapters of Class 6 Maths.

• Chapter 1 Patterns in Mathematics
• Chapter 2 Lines and Angles
• Chapter 3 Number Play
• Chapter 4 Data Handling and Presentation
• Chapter 5 Prime Time
• Chapter 6 Perimeter and Area
• Chapter 7 Fractions
• Chapter 8 Playing with Constructions
• Chapter 9 Symmetry
• Chapter 10 the Other Side of Zero

NCERT Solutions for Class 6 – All Subjects

Just like Chapter 2 of Maths, you can get the exercise questions with answers for every other subject of Class 6. Here are the NCERT Solutions for all subjects of Class 6.

• English
• Hindi
• Maths
• Sanskrit
• Science
• Social Science

NCERT Solutions for Class 6 Maths Chapter 2 – An Overview

The key highlights of this study material are as follows.

Aspects	Details
Class	Class 6
Subject	Maths
Chapter Number	Chapter 2
Chapter Name	Lines and Angles
Book Name	Ganita Prakash
Book By	NCERT (National Council of Educational Research and Training)
Educational Resource Here	NCERT Solutions of Class 6 Maths Chapter 2 for all exercises
More Questions Answers of This Subject	NCERT Solutions for Class 6 Maths
Download Book Chapter	NCERT Book Class 6 Maths
All Questions Answers For This Class	NCERT Solutions for Class 6
Complete Solutions	NCERT Solutions

NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles – FAQs

What are the NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles?

They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 2 Lines and Angles from the NCERT Class 6 Maths textbook Ganita Prakash, written by experts as per the latest NCERT syllabus.

How can I download the Class 6 Maths Chapter 2 solutions PDF for free?

Open this page on aglasem, read the Lines and Angles questions with answers, and click the “Download Solutions PDF” link. The Class 6 Maths Chapter 2 NCERT Solutions PDF is completely free to download.

Are these NCERT Solutions as per the latest 2026-27 syllabus?

Yes. The NCERT Solutions for Class 6 Maths Chapter 2 are based on the latest NCERT textbook Ganita Prakash and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.

Where can I get NCERT Solutions for the other chapters of Class 6 Maths?

You can find the answers to every chapter on the NCERT Solutions for Class 6 Maths page, and solutions for every subject on the NCERT Solutions for Class 6 page.

How do NCERT Solutions help in exam preparation?

They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 6 Maths.

If you have any queries on NCERT Solutions for Class 6 Maths Chapter 2 Lines and Angles, then please ask in the comments below.