Class: 6 Chapter: 2 LINES AND ANGLES – WORKSHEET-2 answer key

LINES AND ANGLES – ANSWER KEY

Class 6 | Chapter 2 | Total Questions: 52

📘 Topic-wise Answer Key with Explanations & Competencies

1. Understanding Points, Lines, Line Segments, and Rays

Competency: Identify and differentiate between basic geometrical figures.

Answers:
a)

• Point: A point represents a location. It has no length, breadth, or thickness. Example: Dot (.)

• Line: A straight path extending in both directions without end. Example: AB↔

• Line Segment: A part of a line with two endpoints. Example: AB

• Ray: A part of a line with one endpoint, extending endlessly in one direction. Example: AB→

b) Correct Answer: b) AB→

c)

• a) False (A line has no endpoints; it extends indefinitely.)

• b) False (A point has no length.)

d) Diagrams to be drawn:

• Two rays with common endpoint (O): OA→ and OB→

• Two intersecting lines: Lines AB↔ and CD↔ intersecting at point P

e) Correct Answer: a) One

---

2. Intersecting and Parallel Lines

Competency: Visualize intersecting and parallel lines in real life.

Answers:
a) Intersecting Lines: Lines that meet at a point.
b) Parallel Lines: Lines that never meet, even if extended. Example: Railway tracks.
c) Draw 2 pairs of parallel lines: AB‖CD and EF‖GH

d)

• a) Parallel

• b) Intersecting

e) Correct Answer: c) A is true, R is false

---

3. Angles and Their Types

Competency: Identify, classify, and measure angles.

Answers:
a) An angle is formed when two rays meet at a point (vertex).
b) Vertex: The common endpoint of two rays forming an angle.

c) Matching:

• Acute angle → (ii) less than 90°

• Right angle → (i) 90°

• Obtuse angle → (iii) greater than 90° and less than 180°

d) Diagrams to be drawn for each angle.

e)

• a) Reflex

• b) Straight

---

4. Pair of Angles

Competency: Understand complementary, supplementary, adjacent, and vertically opposite angles.

Answers:
a) Complementary angles: Sum = 90°. Example: 60° and 30°.
b) Supplementary angles: Sum = 180°. Example: 110° and 70°.

c) Complement of 35° = 55°
d) ∠Y = 180° - 60° = 120°
e) Adjacent angles diagram: Two angles sharing a common side.

---

5. Properties of Angles on a Straight Line and at a Point

Competency: Apply angle properties to solve problems.

Answers:
a) Sum on straight line = 180°
b) Vertically opposite angles are equal.

c) ∠B = 180° - 120° = 60°
d) Vertically opposite angle of 75° = 75°

e) If one angle is 50°, others are 50°, 130°, 130° (by vertically opposite and linear pair rules).

---

🧠 Competency-Based Questions

6. Application Questions

Competency: Apply geometry concepts in real-life contexts.

Answers:
a) Acute angle
b) Right angle
c) Supplementary angle of 89° = 91°
d) Freehand draw approximately 150°
e) Right angle (90° at 3 PM)

---

7. Assertion-Reasoning

Competency: Analyze statements logically.

Answers:
a) Correct Answer: c) A is false, R is true
b) Correct Answer: a) Both A and R are correct and R explains A
c) Correct Answer: a) Both A and R are correct and R explains A
d) Correct Answer: a) Both A and R are correct and R explains A

---

8. Case Study Based

Competency: Analyze geometrical concepts in practical situations.

Case Study 1:
a) Acute and obtuse angles.
b) Yes, vertically opposite angles are equal. Example: 50°-50°, 130°-130°
c) Typically 10 acute angles in a star.

Case Study 2:
a) Intersecting lines (diagonals), parallel lines (sides), right angles (corners).
b) Diagonals can form obtuse angles (more than 90°) inside rectangles.
c) Sum = 360°

---

9. Higher Order Thinking Skills (HOTS)

Competency: Apply reasoning and justify answers.

Answers:
a) Draw X and Y axis meeting at 90°.
b) No. Both obtuse angles > 90°. Their sum > 180°.
c) Example: Scissors blades, crossed roads.
d) Sum of other two angles = 90°
e) 3x + x = 180° ⇒ 4x = 180° ⇒ x = 45°

---

10. Mixed MCQs & Fill in the Blanks

Competency: Recall facts, apply properties.

Answers:
a) c) AB
b) Parallel
c) Complete/Full angle
d) One
e) Let one angle be x, other = 2x
x + 2x = 180° → 3x = 180° → x = 60°, 120°

Class: 6 Chapter: 2 LINES AND ANGLES – WORKSHEET-1

 

📝 LINES AND ANGLES – WORKSHEET

Class: 6
Chapter: 2 – Lines and Angles
Total Questions: 52
Types: Objective, Very Short Answer, Short Answer, Case-based, Assertion-Reasoning

---

📘 Topic-wise Question Bank

---

📌 1. Understanding Points, Lines, Line Segments, and Rays

Competency: Identify and differentiate between basic geometrical figures.

1. Define the following with examples:
   a) Point
   b) Line
   c) Line Segment
   d) Ray

2. Which of the following represents a ray?
   a) AB↔
   b) AB→
   c) AB←→
   d) AB

3. True or False:
   a) A line has two endpoints.
   b) A point has a definite length.

4. Draw a diagram to show:
   a) Two rays with a common endpoint.
   b) Two intersecting lines.

5. Multiple Choice: How many lines can be drawn through two distinct points?
   a) One
   b) Two
   c) Infinite
   d) None

---

📌 2. Intersecting and Parallel Lines

Competency: Visualize intersecting and parallel lines in real life.

6. Define intersecting lines.

7. Define parallel lines with a real-life example.

8. Draw two pairs of parallel lines and label them.

9. Identify whether the following pairs of lines are intersecting or parallel.
   a) Railway tracks
   b) Scissors blades

10. Assertion (A): Railway tracks are parallel lines.
    Reason (R): Parallel lines meet at some point.
    a) A and R are true, and R is correct explanation of A
    b) A and R are true, but R is not correct explanation of A
    c) A is true, R is false
    d) A is false, R is true

---

📌 3. Angles and Their Types

Competency: Identify, classify, and measure angles.

11. Define an angle.

12. What is the vertex of an angle?

13. Match the following:

• Acute angle → (i) 90°

• Right angle → (ii) less than 90°

• Obtuse angle → (iii) greater than 90° and less than 180°

14. Draw one angle of each type: acute, obtuse, right, straight, reflex.

15. Fill in the blanks:
    a) An angle more than 180° but less than 360° is called a ______ angle.
    b) An angle of 180° is called a ______ angle.

---

📌 4. Pair of Angles

Competency: Understand complementary, supplementary, adjacent, and vertically opposite angles.

16. Define complementary angles. Give one pair.

17. Define supplementary angles. Give one pair.

18. If ∠A = 35°, what is its complement?

19. If ∠X + ∠Y = 180°, and ∠X = 60°, find ∠Y.

20. Draw and show a pair of adjacent angles.

---

📌 5. Properties of Angles on a Straight Line and at a Point

Competency: Apply angle properties to solve problems.

21. What is the sum of angles on a straight line?

22. State the vertically opposite angle property.

23. Find the missing angle:
    ∠A + ∠B = 180°, ∠A = 120°.

24. Find the vertically opposite angle of 75°.

25. In a figure, if two lines intersect and one angle is 50°, find all other angles.

---

🧠 Competency-Based Questions

---

📘 6. Application Questions

26. Ria opens a book and notices the angle between the two pages is around 40°. What type of angle is it?

27. A ladder leans against a wall forming an angle of 90° with the ground. What type of angle is this?

28. Find the supplementary angle of 89°.

29. Estimate and draw an angle of approximately 150°.

30. The hour and minute hands of a clock at 3 PM form what kind of angle?

---

📘 7. Assertion-Reasoning Type

31. Assertion (A): Two lines can intersect at two points.
    Reason (R): Lines can bend in space.
    a) Both A and R are correct and R explains A
    b) Both A and R are correct but R doesn’t explain A
    c) A is false, R is true
    d) A is true, R is false

32. Assertion (A): A straight angle measures 180°.
    Reason (R): Straight angle lies on a straight line.
    a) Both A and R are correct and R explains A
    b) Both A and R are correct but R doesn’t explain A
    c) A is false, R is true
    d) A is true, R is false

33. Assertion (A): All vertically opposite angles are equal.
    Reason (R): They are formed by intersecting lines.
    Choose the correct option.

34. Assertion (A): An acute angle can never be a supplementary angle.
    Reason (R): Acute angle is less than 90°.

---

📘 8. Case Study Based

Case Study 1:

Priya made a star using sticks. She noticed many intersecting lines and angles at the center of the star.
35. Identify at least two types of angles formed at the center.
36. Are there any vertically opposite angles? Prove with values.
37. How many acute angles can be formed in such a star?

Case Study 2:

In a classroom, the blackboard is rectangular and mounted flat on the wall. A diagonal is drawn.
38. Identify all the types of lines and angles in the figure.
39. Is the diagonal forming any right or obtuse angles? Justify.
40. Find the sum of all angles inside the rectangle.

---

📘 9. Higher Order Thinking Skills (HOTS)

41. Draw two rays that make exactly 90° angle without using a protractor.

42. Can two obtuse angles be supplementary? Explain with a counterexample.

43. Give two real-life examples where vertically opposite angles are observed.

44. A triangle has one right angle. What is the sum of the other two angles?

45. A straight line forms two adjacent angles. One is 3x and the other is x. Find x.

---

📘 10. Mixed MCQs & Fill in the Blanks

46. Which of the following is not an angle?
    a) ∠A
    b) 90°
    c) AB
    d) ∠XYZ

47. Lines that never meet are called ________.

48. An angle of 360° is called a ________ angle.

49. A ray has ______ endpoint(s).

50. Two angles are supplementary. One is twice the other. Find both.

CLASS 6 CH -1 & 2 HOME TEST JULY 2025-26

 

                                                HOME TEST JULY 2025-26

Q1: The next number in the sequence: 1, 4, 9, 16, 25____ (F/B)                                    (1Mark)

Q2. What comes next ______?                                                 (1 Mark)

     

Q3. Number of points in the following figure are_____                                                        (1 Mark)

 

Q4. The meeting point of a pair of arms of an angle is called ______                                    (1 Mark)

Q5. Rihan marked one point on a piece of paper. How many different lines can he draw that pass

through the point?                                                                                                             (1 Mark)

Q6. Write any two sequences of powers                                                                          (1 Mark)               

Q7. Write first four triangular numbers and show any one of them pictorially                 (2 Marks) 

Q8. Continue the pattern for the next three terms: 1, 2, 4, 8,   ___, ___, ___.                (3 Marks)  

Q9. . Match the items of column A in column B with their respective values                  (4 Marks)

COLUMN A	COLUMN B
(A) The line segment joiining points A and B is denoted by	(i) vertex
(B) Meeting point of a pair of sides is called	(ii)
(C)  A Ray PQ is denoted by	(iii) Acute angle
(D) Angle measure of less than 900  is called	(iv)

  

 

 

ASSERTION-REASONING WORKSHEET CH-10 The Other Side of Zero CLASS 6

  ASSERTION-REASONING WORKSHEET CH-10 The Other Side of Zero CLASS 6

ASSERTION-REASONING WORKSHEET

Chapter: The Other Side of Zero (Integers)                FOR DOWNLOAD PDF CLICK HERE
Class: 6 | NCERT Maths Chapter 10

✍🏽 Choose the correct option:
(A) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true, but Reason is not the correct explanation.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

---

Q1.

Assertion (A): Integers include positive numbers, negative numbers, and zero.
Reason (R): Integers are only the numbers greater than zero.
Option: ___

---

Q2.

Assertion (A): The opposite of +7 is −7.
Reason (R): Opposite integers are at equal distance from zero but on opposite sides.
Option: ___

---

Q3.

Assertion (A): Zero is a positive integer.
Reason (R): Zero lies to the right of all negative numbers on the number line.
Option: ___

---

Q4.

Assertion (A): −3 is smaller than −2.
Reason (R): On a number line, numbers towards the left are smaller.
Option: ___

---

Q5.

Assertion (A): Integers can be represented on a number line.
Reason (R): Each integer has a fixed position on the number line.
Option: ___

---

Q6.

Assertion (A): The sum of two negative integers is a positive integer.
Reason (R): Negative plus negative makes the number smaller.
Option: ___

---

Q7.

Assertion (A): Zero has no sign.
Reason (R): Zero is neither positive nor negative.
Option: ___

---

Q8.

Assertion (A): The opposite of 0 is 0.
Reason (R): Zero is at the center of the number line and has no direction.
Option: ___

---

Q9.

Assertion (A): −8 + (+3) = −5
Reason (R): Adding a positive number to a negative number shifts to the right on the number line.
Option: ___

---

Q10.

Assertion (A): −2 − (−3) = 1
Reason (R): Subtracting a negative number is same as adding its positive.
Option: ___

---

Q11.

Assertion (A): −10 is greater than −9.
Reason (R): Greater negative number means greater value.
Option: ___

---

Q12.

Assertion (A): (−4) + (−5) = −9
Reason (R): When two negative numbers are added, their sum is also negative.
Option: ___

---

Q13.

Assertion (A): Addition of two integers always results in a larger integer.
Reason (R): Adding any two numbers always increases value.
Option: ___

---

Q14.

Assertion (A): Integers are closed under subtraction.
Reason (R): Subtracting any two integers always gives another integer.
Option: ___

---

Q15.

Assertion (A): Zero is the identity for addition of integers.
Reason (R): Adding zero to any integer doesn’t change its value.
Option: ___

---

Q16.

Assertion (A): On the number line, the farther a negative number is from zero, the smaller it is.
Reason (R): Distance from zero increases negativity.
Option: ___

---

Q17.

Assertion (A): The sum of a number and its opposite is always zero.
Reason (R): Opposites cancel each other on the number line.
Option: ___

---

Q18.

Assertion (A): The result of subtracting a positive integer from a negative integer is always negative.
Reason (R): Subtracting a positive makes a number smaller.
Option: ___

---

Q19.

Assertion (A): Integers help in representing real-life situations like gains and losses.
Reason (R): Positive and negative numbers can represent profit and loss respectively.
Option: ___

---

Q20.

Assertion (A): −1 is the greatest negative integer.
Reason (R): On the number line, −1 is closest to zero among all negative numbers.
Option: ___
ANSWER KEY CLICK HERE