Class 6 Maths – Chapter 2: Lines and Angles - Case-Based Study Questions

 

Class 6 Maths – Chapter 2: Lines and Angles

🎓 Case-Based Study Questions

---

🧾 Case Study 1: The Clock Shop

Case:
Riya visits a clock shop and observes different wall clocks showing various times. She notices the angles formed between the hour and minute hands.

Clock	Time Displayed	Observation
A	3:00	Hands form a 90° angle
B	6:00	Hands form a straight line
C	2:00	Hands form an acute angle

Questions:

1. What type of angle is formed in Clock A?
   a) Acute
   b) Obtuse
   c) Right
   d) Straight
   ✅ Answer: c) Right

2. What is the measure of the angle in Clock B?
   a) 90°
   b) 180°
   c) 120°
   d) 45°
   ✅ Answer: b) 180°

3. In Clock C, the angle formed is less than 90°. What type of angle is this?
   ✅ Answer: Acute angle

4. Write the name of two objects in your house that show right angles like Clock A.
   ✅ Answer: Examples may include corners of books, TV screens, tiles, etc.

---

📏 Case Study 2: The Road Intersection

Case:
Two roads cross each other near Aryan’s school. The municipal engineer says they intersect perpendicularly. Aryan sees four equal angles formed at the intersection.

Questions:

1. What is the measure of each angle formed?
   ✅ Answer: 90°

2. What are such angles called?
   ✅ Answer: Right angles

3. What is the relationship between the two roads?
   a) Parallel
   b) Intersecting
   c) Perpendicular
   d) Skew
   ✅ Answer: c) Perpendicular

4. How many right angles are formed when two perpendicular lines cross?
   ✅ Answer: 4

5. Draw and label two perpendicular lines using a ruler and a set square.
   ✅ (Student drawing question)

---

📐 Case Study 3: Art Class Geometry

Case:
During an art activity, Meera draws two lines that never meet, even if extended. She decorates the space between them and labels the lines as AB and CD.

Questions:

1. What is the relationship between line AB and line CD?
   ✅ Answer: Parallel lines

2. Can parallel lines ever intersect?
   ✅ Answer: No

3. Meera now draws a third line EF that cuts both AB and CD. What is EF called?
   ✅ Answer: Transversal

4. When a transversal cuts two parallel lines, what types of angles are formed?
   ✅ Answer: Corresponding, alternate interior, alternate exterior angles

5. Identify one real-life example of parallel lines from your surroundings.
   ✅ Answer: Railway tracks, lines on a ruled notebook, edge of a table

---

🎯 Case Study 4: Building the School Fence

Case:
While helping to install the school fence, students used measuring tapes and set squares to form corners. They ensured every corner was at a right angle.

Questions:

1. Why did they use a set square for the corners?
   ✅ Answer: To form right angles accurately

2. How many degrees is a right angle?
   ✅ Answer: 90°

3. If four corners of the school fence are each right angles, what shape is formed?
   ✅ Answer: Rectangle or square

4. If one corner was more than 90°, what type of angle would it be?
   ✅ Answer: Obtuse angle

5. Which tool can you use to measure any angle?
   ✅ Answer: Protractor

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)