| Class: VI |
Subject: Mathematics |
Session: 2025-26 |
| Chapter: 02 - Lines and Angles |
Time: 1½ Hours |
Max. Marks: 40 |
General Instructions:
- All questions are compulsory.
- This question paper contains 20 questions divided into five sections A, B, C, D and E.
- Section A contains 10 MCQs of 1 mark each.
- Section B contains 4 questions of 2 marks each.
- Section C contains 3 questions of 3 marks each.
- Section D contains 1 question of 5 marks.
- Section E contains 2 Case Study Based questions of 4 marks each.
Q1. A point determines a:
(a) Line
(b) Location
(c) Angle
(d) Distance
Q2. How many lines can pass through two distinct points?
(a) Only one
(b) Two
(c) Infinite
(d) None
Q3. A right angle measures:
(a) 45°
(b) 90°
(c) 180°
(d) 360°
Q4. An angle measuring 125° is:
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Reflex angle
Q5. One complete rotation equals:
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Q6. A straight angle measures:
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Q7. An acute angle is:
(a) Equal to 90°
(b) Less than 90°
(c) Greater than 90°
(d) Equal to 180°
Q8. A reflex angle is:
(a) Less than 90°
(b) Between 90° and 180°
(c) Between 180° and 360°
(d) Exactly 180°
Q9. At 3 o'clock, the angle between hour and minute hands is:
(a) 45°
(b) 90°
(c) 120°
(d) 180°
Q10. An angle is formed by:
(a) One ray
(b) One line
(c) Two rays with a common starting point
(d) Two parallel lines
Q11. What is the difference between a line segment and a line? Draw both.
Q12. Draw any angle and name it with vertex O. Label its arms and vertex properly.
Q13. A wheel is divided into 12 equal parts by spokes. Find the angle between any two consecutive spokes.
Q14. What is the angle formed by the hands of a clock at 6 o'clock? What type of angle is it?
Q15. Classify the following angles as acute, obtuse, right, or reflex: 45°, 120°, 90°, 200°, 75°, 270°
Q16. Draw any triangle ABC. Name all the angles formed in the triangle.
Q17. A straight angle AOB is divided into two parts such that ∠AOC = 65°. Find ∠BOC. What type of angle is ∠BOC?
Q18.
(a) Define the following with examples: Acute angle, Obtuse angle, Right angle, Reflex angle
(b) Draw one example of each type of angle
(c) Measure each angle you have drawn using a protractor
Q19. Case Study 1: Clock Tower
A famous clock tower in the city shows different angles between its hour and minute hands at different times. The hands move continuously around the clock face.
Based on the above information, answer the following:
(a) At 1 o'clock, what is the angle between the hour and minute hands? (1 mark)
(b) At what time do both hands form a right angle between 12 and 3? (1 mark)
(c) What type of angle is formed at 4 o'clock? (1 mark)
(d) Through how many degrees does the minute hand move in 15 minutes? (1 mark)
Q20. Case Study 2: Traffic Junction
Four roads meet at a traffic junction forming different angles. Three of the angles measure 85°, 90°, and 95°. Let the fourth angle be x.
Based on the above information, answer the following:
(a) What is the sum of all angles at the junction? (1 mark)
(b) Find the value of x. (1 mark)
(c) Which angle is the smallest and which is the largest? (1 mark)
(d) Identify the type of each angle formed. (1 mark)
Q1. (b) Location
A point determines a specific location or position in space.
Q2. (a) Only one
Through two distinct points, only one unique line can be drawn.
Q3. (b) 90°
A right angle always measures exactly 90 degrees.
Q4. (c) Obtuse angle
An angle between 90° and 180° is called an obtuse angle. 125° falls in this range.
Q5. (d) 360°
One complete rotation around a point equals 360 degrees.
Q6. (b) 180°
A straight angle measures exactly 180 degrees.
Q7. (b) Less than 90°
An acute angle is any angle that measures less than 90 degrees.
Q8. (c) Between 180° and 360°
A reflex angle is greater than 180° but less than 360°.
Q9. (b) 90°
At 3 o'clock, the hour hand is at 3 and the minute hand is at 12, forming a right angle of 90°.
Q10. (c) Two rays with a common starting point
An angle is formed when two rays share a common starting point called the vertex.
Q11.
Line Segment: A line segment has two endpoints and a definite length. It is the shortest distance between two points.
Line: A line extends infinitely in both directions and has no endpoints. It has no definite length.
[Students should draw both with proper labels - line segment AB with two dots at endpoints, and line PQ with arrows on both ends]
Q12.
[Students should draw an angle with vertex O and two rays extending from it]
The angle can be named as ∠AOB or ∠BOA
Vertex: O (the common starting point)
Arms: OA and OB (the two rays forming the angle)
Q13.
Given: A wheel is divided into 12 equal parts
Solution:
Total angle at center = 360°
Number of parts = 12
Angle between consecutive spokes = 360° ÷ 12 = 30°
Q14.
At 6 o'clock:
The hour hand is at 6 and the minute hand is at 12.
They are in opposite directions on the clock.
Angle formed = 180°
Type: This is a Straight Angle
Q15.
Classification of angles:
• 45° - Acute angle (less than 90°)
• 120° - Obtuse angle (between 90° and 180°)
• 90° - Right angle (exactly 90°)
• 200° - Reflex angle (between 180° and 360°)
• 75° - Acute angle (less than 90°)
• 270° - Reflex angle (between 180° and 360°)
Q16.
[Students should draw a triangle ABC]
Three angles formed in triangle ABC are:
1. ∠ABC or ∠CBA (angle at vertex B)
2. ∠BCA or ∠ACB (angle at vertex C)
3. ∠CAB or ∠BAC (angle at vertex A)
Q17.
Given:
AOB is a straight angle
∠AOC = 65°
To find: ∠BOC
Solution:
Since AOB is a straight angle:
∠AOB = 180°
∠AOC + ∠BOC = 180°
65° + ∠BOC = 180°
∠BOC = 180° - 65°
∠BOC = 115°
Type: Since 115° is greater than 90° but less than 180°, it is an Obtuse angle
Q18.
(a) Definitions and Examples:
1. Acute Angle: An angle that measures less than 90°
Example: 45°, 60°, 30°
2. Obtuse Angle: An angle that measures more than 90° but less than 180°
Example: 120°, 150°, 110°
3. Right Angle: An angle that measures exactly 90°
Example: Corner of a book, letter L
4. Reflex Angle: An angle that measures more than 180° but less than 360°
Example: 270°, 200°, 300°
(b) Drawings:
[Students should draw four different angles - one of each type]
• Draw an acute angle (e.g., 60°)
• Draw an obtuse angle (e.g., 120°)
• Draw a right angle (90°)
• Draw a reflex angle (e.g., 270°)
(c) Measurements:
[Students should use a protractor to measure each angle they have drawn and verify the measurements match the type of angle]
Q19. Case Study 1: Clock Tower
(a) Angle at 1 o'clock:
Hour hand at 1, minute hand at 12
Angle = 1 × 30° = 30°
(b) Time for right angle between 12 and 3:
Right angle = 90°
This occurs at 3 o'clock (when hour hand is at 3 and minute hand is at 12)
(c) Type of angle at 4 o'clock:
Hour hand at 4, minute hand at 12
Angle = 4 × 30° = 120°
Type: Obtuse angle (between 90° and 180°)
(d) Degrees in 15 minutes:
Minute hand completes 360° in 60 minutes
In 15 minutes = (360° ÷ 60) × 15 = 6° × 15 = 90°
Q20. Case Study 2: Traffic Junction
(a) Sum of all angles at junction:
At any point, angles around it sum to 360°
(b) Finding value of x:
85° + 90° + 95° + x = 360°
270° + x = 360°
x = 360° - 270°
x = 90°
(c) Smallest and largest angles:
Smallest angle = 85°
Largest angle = 95°
(d) Type of each angle:
• 85° - Acute angle (less than 90°)
• 90° - Right angle (exactly 90°)
• 95° - Obtuse angle (greater than 90°)
• x = 90° - Right angle (exactly 90°)