NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 2 Solution PDF

NCERT Solutions for Chapter 2 Lines and Angles help students understand how basic geometry is connected to our daily life. This chapter introduces key concepts like points, lines, line segments, rays, and different types of angles we see around us—in objects like books, doors, road signs, and buildings.

It introduces number patterns and sequences, and teaches students how to find the rules behind these patterns. The solutions include simple explanations, clear examples, and step-by-step answers to make it easier for students to spot patterns and solve problems.

These solutions follow the latest Class 6 Maths syllabus and are designed to improve logical thinking and problem-solving skills in a fun and practical way.

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

Chapter 2 Lines and Angles introduces basic geometry concepts that are important in understanding shapes, structures, and designs around us. The chapter begins with simple ideas like points, line segments, lines, and rays, helping students understand how these are formed and related.

It then explains different types of angles – such as acute, obtuse, and right angles – and how to identify them in real life and in drawings. Students also learn how lines can be straight, curved, or intersecting, and how angles are formed when two lines meet.

This chapter lays a strong foundation for geometry by using easy-to-understand language, clear diagrams, and activities. The NCERT solutions provide step-by-step answers to help students practice and improve their understanding of basic geometric ideas, which are useful in both academics and daily life.

Ganita Prakash Class 6 Maths Chapter 2 Solutions Worksheet with Answers

Below are the detailed solutions for Ganita Prakash Class 6 Maths Chapter 2 Lines and Angles. These solutions are designed to help students understand the basic ideas of geometry, such as points, lines, line segments, rays, and angles.

2.1 Point 2.2 Line Segment 2.3 Line 2.4 Ray Figure it Out (Page No. 15-17)

Question 1.

Can you help Rihan and Sheetal find their answers?
Solution:
Rihan can draw infinite number of lines that pass through the point.
Whereas Sheetal can draw only one line that passes through both of the points.

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

Answer:

In the given figure, the line segments are:

• LM

• MP

• PQ

• QR

Now, let’s look at the points:

• Points L and R lie on only one line segment each

• Points M, P, and Q lie on two line segments each because they are the connecting points between two segments.

This means:

• M is on both LM and MP

• P is on both MP and PQ

• Q is on both PQ and QR

These points help form a continuous path using straight line segments.

Question 3.
Name the rays shown in Fig. 2.5. Is T the starting point of each of these rays?

Answer:

In the given Figure 2.5, there are two rays shown. Let’s name them:

• Ray TA (→TA): This ray starts from point T and goes through point A.

• Ray TB (→TB): This ray also starts from point T and goes through point B.

Yes, in both rays, T is the starting point.
In geometry, the starting point of a ray is called the initial point.
So here, T is the initial point of both ray TA and ray TB. 

Question 4.
Draw a rough figure and write labels appropriately to illustrate each of the following:
(a) OP and OQ meet at O.
Solution:

(b) XY and PQ intersect at point M.
Solution:

(c) Line l contains joints E and F but not point D.
Solution:

(d) Point P lies on AB.
Solution:

Question 5.
In the figure, name
(a) five points
(b) a line
(c) four rays
(d) five line segments

(a) The five points shown in the figure are:
D, E, O, C, and B

(b) The line in the figure is:
Line DB (It passes through points D and B and continues in both directions)

(c) The four rays are:
Ray OC, Ray OB, Ray EB, and Ray OD
(All of these start from one point and go in one direction)

(d) The five line segments in the figure are:
DE, EO, OB, DO, and EB
(A line segment connects two points and has a fixed length)

Question 6.

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.

Answer:

(a) No, we cannot name ray OA as ray OB.
A ray has a starting point and goes in one direction forever.

• In ray OA, O is the starting point and it goes through A.

• If you call it ray OB, you're saying it starts at O and goes through B, which is a different direction unless B and A are the same point.

So, ray OB would not be the same as ray OA, unless B is exactly where A is.

(b) No, we cannot write ray OA as ray AO.

• In ray OA, the ray starts at O and goes through A.

• Writing ray AO means you're saying it starts at A and goes through O, which is a different direction.

So, the order of letters matters in naming a ray. The first point is always the starting point.

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.

Answer:

Yes, we can find the angles in the given pictures.

Question 2.

Explain why ∠APC cannot be labelled as ∠P.

Answer:

The angle ∠APC cannot be labelled just as ∠P because three different angles meet at point P.
If we just say ∠P, it won’t be clear which of these three angles we’re talking about.

• One angle is between the lines of PA and PC (this is ∠APC).

• Another angle is between the lines PA and PB (this is ∠APB).

• The third angle is between the lines PB and PC (this is ∠BPC).

Answer

In the given figure, marked angles are ∠RTQ and ∠RTP.

Question 5.

Now, mark any four points on your paper so that no three of them are on one line. Label them A, B, C and 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 and D? Write them all down and mark each of them with a curve as in given figure.

Answer:

Point A, B, C and D are as follow

Possible lines are AB, BC, CD, AD, AC and BD.

Thus, there are six lines formed and angles are ∠BAC, ∠BAD, ∠ADB, ∠ADC, ∠DCA, ∠DCB, ∠ABD, ∠ABC, ∠CAD, ∠BDC, ∠ACB and ∠DBC.

Thus, there are total twelve angles formed.

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?

Answer:

Do it yourself. For your reference, ∠5 is the largest and ∠2 is the smallest among all the angles in the figure shown below.

Question 2.

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.

Answer:

When we compare angles by superimposing them (placing one over the other), we can tell which is bigger, smaller, or equal.

(a) ∠AOB is greater than ∠XOY
Because the size (opening) of ∠AOB is wider than ∠XOY.

(b) ∠AOB is greater than ∠XOB
Because the angle ∠AOB has a larger opening than ∠XOB.

(c) ∠XOB and ∠XOC are equal
  Because they have:

• The same vertex (O)

• A common arm (OX)
  
  And the other arms (OB and OC) overlap
  So, both angles are exactly the same in size.

Question 3.

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

Answer:

On comparing by superimposition, the angles ∠XOY and ∠AOB in the given figure, we get ∠XOY is greater than ∠AOB because size of ∠XOY is greater.

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:
Do it yourself.

Question 2.
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?

Answer: 

We can produce BA beyond A to make a straight angle, then through A, draw the line DE, which is perpendicular to BC as shown in the figure below. Clearly, ∠DAB or ∠EAB is a right angle. There is only one way of doing it.

Question 3.
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.
Answer: 

(a) By folding a second crease that is perpendicular to the slanting crease, we’ll get 4 right angles.
(b) To explain some other person who doesn’t know the process, he can follow the given steps:

• Fold Diagonally: Fold a rectangular sheet of paper by bringing one corner to the opposite corner. Press to create a diagonal crease. Unfold.

• Fold Perpendicular: Lay the paper flat. Fold one edge to meet the diagonal crease, aligning it perfectly. Press to create a perpendicular crease. Unfold.

• Check: The intersection of the two creases should create four right angles (90°) at the crossing point.

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

Question 1.
Make a few acute angles and a few obtuse angles. Draw them in different orientations.
Answer:
Do it yourself.

Question 2.
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 3.

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

Answer:

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

Next figure will be as follows:

Number of acute angles = 21 + 9 = 30

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

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

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!

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?

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:

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.

Answer:

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

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

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.

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.

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.

Answer:
(a) The clock is divided into 12 h, so each hour mark is 30° apart (360°- 12 = 30°).
Therefore, at 1 O’clock the hour hand is at 1 and the minute hand is at 12, forming a 30° angle.

(b) At 2 O’clock, it is 60° (i.e. 30° × 2 = 60°), at 4 O’clock, it is 120° (i.e. 30° × 4 = 120°) and at 6 O’clock, it is 180° (i.e. 30° × 6 = 180°)

(c) The angle increases by 30° for each hour. Other angle includes 90° at 3 O’clock, 150° at 5 O’clock and so on. Thus, on multiplying the hour by 30°, we can find the angle at any hour.

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?

Answer:
Yes, it is possible to express the amount by which a door is opened using an angle. The hinge of the door will be the vertex of the angle. The wall and the door will be the arms of the angle.

Question 3.
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?

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

Question 4.
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.

Answer:
Both insects are rotated 90° clockwise.

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

Question 1.
In the given figure 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.

Answer:

NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 2 PDF Download 

Students can download the NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 2  Lines and Angles in PDF format from the link provided below. These solutions are  created to help students clearly understand the basic concepts of geometry, such as points, lines, line segments, rays, and angles.

The answers include step-by-step explanations, clear diagrams, and easy definitions that support all textbook questions and activities.

Benefits of Using NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 2

 All solutions are written in easy-to-understand words, helping students quickly grasp new terms like ray, line segment, and angle.

 Solutions include complete answers to textbook exercises, diagrams, “Figure it Out” tasks, and drawing-based geometry questions.

 By learning with pictures and line drawings, students begin to recognize angles, lines, and shapes in their surroundings—like road crossings, corners of books, or edges of tables.

 This chapter lays the foundation for understanding geometry in higher classes by teaching students how to read, name, and draw basic shapes and angles.

 Students develop spatial sense and logical thinking—essential skills not only in math but in everyday decision-making too.