Q: 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?

Line segments in Fig. 2.4: $\overline{LM}$, $\overline{MP}$, $\overline{PQ}$ and $\overline{Q R}$Points on exactly one of the line segments: L and RPoints on two of the line segments: M, P, and Q

Q: Name the rays shown in given figure. Is T the starting point of each of these rays?

Rays in the given figure are $\overrightarrow{\mathrm{TA}}, \overrightarrow{\mathrm{TN}}, \overrightarrow{\mathrm{TB}}$ and $\overrightarrow{\mathrm{NB}}$.Yes, T is the starting point of each of these rays in given figure.

Q: 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.

(b) $\overline{\mathrm{XY}}$ and $\overline{\mathrm{PQ}}$ intersect at point M.Solution:(c) Line l contains points E and F but not point D.Solution:(d) Point P lies on AB.Solution:

Q: In Fig. 2.6, name: (a) five points (b) a line (c) four rays (d) five-line segment

Five points: B, C, O, E and DA line: $\overrightarrow{DB}$Four rays: $\overrightarrow{OC}$, $\overrightarrow{OB}$, $\overrightarrow{OD}$ and $\overrightarrow{OX}$[Here, one ray has been drawn and the continued point has not been named; thus, we have named it X. Thus, the fourth ray is $\overrightarrow{OX}$]Five line segments: $\overrightarrow{DE}$, $\overrightarrow{EO}$, $\overrightarrow{BO}$, $\overrightarrow{DO}$ and $\overrightarrow{CO}$

Q: Here, a ray $\overrightarrow{O A}$ in given figure. It starts at 0 and passes through the point A. It also passes through the point B. (a) Can you also name it as $\overrightarrow{O B}$? Why? (b) Can we write $\overrightarrow{O B}$ as $\overrightarrow{A O}$? Why or why not?

(a) Yes, we can also name of ray $\overrightarrow{O A}$ as ray $\overrightarrow{O B}$ because initial point of both is same and going on endlessly in the same direction.(b) No, we cannot not write $\overrightarrow{O A}$ as $\overrightarrow{A O}$ because initial point of a ray cannot be changed.2.5 Angle Figure it Out (Page No. 19-21)

Q: 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 Fig. 2.9.

Number of lines = 6; $\overleftrightarrow{AB}$, $\overleftrightarrow{BC}$, $\overleftrightarrow{CD}$, $\overleftrightarrow{AD}$, $\overleftrightarrow{AC}$ and $\overleftrightarrow{BD}$The number of angles (including A, B, C, and D) = 12; ∠ABC, ∠ABD, ∠DBC, ∠BCD, ∠BCA, ∠ACD, ∠CDA, ∠CDB, ∠BDA, ∠DAB, ∠DAC, and ∠BAC.2.6 Comparing Angles Figure it Out (Page No. 23)

Question 1

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?

Accepted 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.

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Rihan, Marked, Point, Piece, Paper, Lines. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ10: Name the angles marked in the given figure.
Q11: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible...
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 2

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?

Accepted Answer

Line segments in Fig. 2.4: $\overline{LM}$, $\overline{MP}$, $\overline{PQ}$ and $\overline{Q R}$Points on exactly one of the line segments: L and RPoints on two of the line segments: M, P, and Q

Question 3

Name the rays shown in given figure. Is T the starting point of each of these rays?

Accepted Answer

Rays in the given figure are $\overrightarrow{\mathrm{TA}}, \overrightarrow{\mathrm{TN}}, \overrightarrow{\mathrm{TB}}$ and $\overrightarrow{\mathrm{NB}}$.Yes, T is the starting point of each of these rays in given figure.

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.

Accepted Answer

(b) $\overline{\mathrm{XY}}$ and $\overline{\mathrm{PQ}}$ intersect at point M.Solution:(c) Line l contains points E and F but not point D.Solution:(d) Point P lies on AB.Solution:

Question 5

In Fig. 2.6, name:
(a) five points
(b) a line
(c) four rays
(d) five-line segment

Accepted Answer

Five points: B, C, O, E and DA line: $\overrightarrow{DB}$Four rays: $\overrightarrow{OC}$, $\overrightarrow{OB}$, $\overrightarrow{OD}$ and $\overrightarrow{OX}$[Here, one ray has been drawn and the continued point has not been named; thus, we have named it X. Thus, the fourth ray is $\overrightarrow{OX}$]Five line segments: $\overrightarrow{DE}$, $\overrightarrow{EO}$, $\overrightarrow{BO}$, $\overrightarrow{DO}$ and $\overrightarrow{CO}$

Question 6

Here, a ray $\overrightarrow{O A}$ in given figure. It starts at 0 and passes through the point A. It also passes through the point B.
(a) Can you also name it as $\overrightarrow{O B}$? Why?
(b) Can we write $\overrightarrow{O B}$ as $\overrightarrow{A O}$? Why or why not?

Accepted Answer

(a) Yes, we can also name of ray $\overrightarrow{O A}$ as ray $\overrightarrow{O B}$ because initial point of both is same and going on endlessly in the same direction.(b) No, we cannot not write $\overrightarrow{O A}$ as $\overrightarrow{A O}$ because initial point of a ray cannot be changed.2.5 Angle Figure it Out (Page No. 19-21)

Question 7

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.

Accepted Answer

(a) ∠ADB, ∠BDC, vertex: D(b) ∠PQR, vertex: Q(c) ∠LMN, vertex: M(d) ∠XYZ, vertex: Y

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Angles, Pictures, Rays, Forming, Vertex, Angle. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ10: Name the angles marked in the given figure.
Q11: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible...
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 8

Explain why ∠APCcannot be labelled as ∠P?

Accepted Answer

In the given figure, PB divides ∠APC in two parts and . makes two angles ∠APB and ∠CPB.So, ∠APC is greater than ∠APB and ∠CPB.Therefore, ∠APC cannot be labelled as ∠P.

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Apccannot, Lines and Angles, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ10: Name the angles marked in the given figure.
Q11: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible...
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 9

Name the angles marked in the given figure.

Accepted Answer

The three angles marked in the figure are ∠PTQ, ∠QTR, and ∠PTR.

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Angles, Marked, Figure, Lines and Angles, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ11: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible...
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Q15: Which angle is greater: ∠XOY or ∠AOB? Give reasons.
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 10

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).

Accepted Answer

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

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Mark, Points, Paper, Line, Possible, Lines. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ10: Name the angles marked in the given figure.
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Q15: Which angle is greater: ∠XOY or ∠AOB? Give reasons.
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 11

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 Fig. 2.9.

Accepted Answer

Number of lines = 6; $\overleftrightarrow{AB}$, $\overleftrightarrow{BC}$, $\overleftrightarrow{CD}$, $\overleftrightarrow{AD}$, $\overleftrightarrow{AC}$ and $\overleftrightarrow{BD}$The number of angles (including A, B, C, and D) = 12; ∠ABC, ∠ABD, ∠DBC, ∠BCD, ∠BCA, ∠ACD, ∠CDA, ∠CDB, ∠BDA, ∠DAB, ∠DAC, and ∠BAC.2.6 Comparing Angles Figure it Out (Page No. 23)

Question 12

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?

Accepted Answer

Let’s mark the rectangle and vertex of the fold as shown in figure below.We get ∠1, ∠2, ∠3 and ∠4.Comparing: ∠1 ∠1 = ∠4, ∠2 = ∠3.∠2 and ∠3 are the largest angles.∠1 and ∠4 are the smallest angles.

Question 13

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 how you decided which one is greater.

Accepted Answer

(a) ∠AOB > ∠XOY; it is visible that ∠XOY is included within ∠AOB, so ∠AOB > ∠XOY.(b) ∠AOB > ∠XOB; it is visible that arms OA and OB are open more than arms OX and OB also, ∠XOB is included within ∠AOB.(c) ∠XOB = ∠XOC; here, the arm OX is common, and the points B and C lie on the same arm thus, ∠XOB = ∠XOC.

Question 14

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

Accepted Answer

Here, ∠XOY > ∠AOB.Using the superimposition method, we can see that ∠XOY > ∠AOB.Alternatively, it can be seen that the gap between arms OA and OX is greater than the gap between arms OY and OB, thus making the ∠XOY > ∠AOB.

Question 15

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

Accepted Answer

Using a single letter name like ∠P is insufficient in case of two or more angles having the same vertex. Here, ∠P can be considered for any of the three angles ∠APB, ∠BPC or ∠APC. So, here it is necessary to use three letters in specifying an angle.2.7 Making Rotating Arms 2.8 Special Types of Angles Figure it Out (Page No. 29-31)

Question 16

How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom?

Accepted Answer

A window has 4 right angles.∠1, ∠2, ∠3 and ∠4.Yes. At comers of door. At comers of blackboard etc.

Source: This question is from Lines and Angles, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Lines and Angles: Right, Angles, Windows, Classroom, Contain, See. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Lines and AnglesQ10: Name the angles marked in the given figure.
Q11: Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible...
Q12: Now mark any four points on your paper so that no three of them are on one line. Label them A, B,...
Q13: Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the...
Q14: In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB...
Practice more questions from Lines and Angles &mdash; Mathematics, Class 6 CBSE

Question 17

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?

Accepted Answer

A straight angle is formed when two points are connected by a straight line, making the angle measure 180°. In simpler terms, it’s a line that continues straight without turning.To create a straight angle using point A, we need to draw a straight line from A to another grid point in such a way that the line extends in both directions and passes through A.Horizontal Line: Connecting A to a grid point directly to the left or right of A.Vertical Line: Connecting A to a grid point directly above or below A.Diagonal Lines: Connecting A to grid points diagonally (northeast to southwest or northwest to southeast).

Question 18

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 does not know the process can simply follow your description to get the right angle.

Accepted Answer

(a) You will have four right angles now.Explanation When you fold the paper to create a crease that is perpendicular to the first, the two creases intersect at a right angle dividing the plane into four right angles of 90° each.(b) To create a right angleI. First fold Start by folding the paper so that one corner meets the opposite edge, creating a slant crease.II. Second fold Now, fold the paper again but this time align the planting crease with the edge of the paper, ensuring the fold is perpendicular to the first crease.III. Unfold When you open the paper, you will see that the two creases intersect at a 90° angle, forming four right angles.Explanation The second fold must be made carefully, aligning the first crease with the edge of the paper to insure the two creases are perpendicular. This guarantees that the angles formed are exactly 90°.2.7 Making Rotating Arms 2.8 Special Types of Angles Figure it Out (Page No. 31-32)

Question 19

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

Accepted Answer

The student needs to measure the angles on their own using their protractors by keeping the center at H in each case and aligning one arm in such a way that it passes through 0°.Yes, the paper protractor can be used to measure these angles.

Question 20

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

Accepted Answer

Using a protractor, the angle can be measured in the following way:We know that the complete angle measure is 360°, and here, the external angle needs to be measured. The interior angle can be measured using the protractor and must be subtracted from 360° to find the exterior angle. Such angles are known as reflex angles.InText Questions (Page 34)