| 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 ray has:
(a) Two endpoints
(b) One endpoint
(c) No endpoint
(d) Three endpoints
Q2. How many lines can pass through a single point?
(a) Only one
(b) Two
(c) Ten
(d) Infinite
Q3. An angle measuring 47° is:
(a) Acute angle
(b) Obtuse angle
(c) Right angle
(d) Straight angle
Q4. Half of a straight angle is:
(a) 45°
(b) 90°
(c) 135°
(d) 180°
Q5. The instrument used to measure angles is called:
(a) Compass
(b) Divider
(c) Protractor
(d) Ruler
Q6. An angle of 200° is called:
(a) Acute angle
(b) Obtuse angle
(c) Reflex angle
(d) Complete angle
Q7. Which of the following is NOT a geometric term?
(a) Point
(b) Line
(c) Circle
(d) Height
Q8. The common point where two rays meet to form an angle is called:
(a) Arm
(b) Vertex
(c) End point
(d) Starting point
Q9. If ∠A = 85° and ∠B = 95°, then ∠A + ∠B equals:
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Q10. The shortest distance between two points is called:
(a) A line
(b) A ray
(c) A line segment
(d) An angle
Q11. What is a ray? Give two examples from real life where you can see a ray.
Q12. Two angles measure 55° and 35°. Find their sum. What is the type of the resulting angle?
Q13. The Ashoka Chakra has 24 spokes. Find the angle between any two consecutive spokes.
Q14. Can we have a triangle with all three angles as acute angles? Justify your answer with an example.
Q15. Draw four points A, B, C, and D such that no three points are collinear. Join them in order to form a quadrilateral ABCD. Name any four angles formed in this figure.
Q16. An angle is 28° more than its complement. Find both angles. (Note: Two angles are complementary if their sum is 90°)
Q17. A complete angle is divided into four parts in the ratio 2:3:4:6. Find the measure of each part. Identify the type of each angle formed.
Q18.
(a) Explain what you understand by angle bisector with a diagram.
(b) Draw an angle of 120° using a protractor.
(c) Using paper folding method, draw its angle bisector.
(d) Measure the two angles formed after bisection.
(e) What type of angles are these?
Q19. Case Study 1: Pizza Slices
Ravi ordered a circular pizza of 12 inches diameter. The pizza is cut into 8 equal slices. Each slice forms an angle at the center of the pizza.
Based on the above information, answer the following:
(a) What is the angle formed by each slice at the center? (1 mark)
(b) If Ravi eats 3 slices, what is the total angle covered? (1 mark)
(c) What type of angle is formed when 3 slices are put together? (1 mark)
(d) How many slices should be eaten to form a straight angle? (1 mark)
Q20. Case Study 2: Ferris Wheel
A Ferris wheel at an amusement park has 15 equally spaced cabins arranged in a circle. The wheel rotates around its center.
Based on the above information, answer the following:
(a) What is the angle between two consecutive cabins? (1 mark)
(b) If you are in cabin 1 and your friend is in cabin 6, what is the angle between your positions? (1 mark)
(c) When the wheel completes half rotation, through what angle does a cabin move? (1 mark)
(d) What type of angle is formed between cabin 1 and cabin 4? (1 mark)
Q1. (b) One endpoint
A ray starts at one point and extends infinitely in one direction. It has exactly one endpoint.
Q2. (d) Infinite
Through a single point, infinite lines can pass in all possible directions.
Q3. (a) Acute angle
An angle less than 90° is called an acute angle. Since 47° < 90°, it is acute.
Q4. (b) 90°
A straight angle = 180°. Half of 180° = 180° ÷ 2 = 90° (right angle).
Q5. (c) Protractor
A protractor is the instrument used to measure angles in degrees.
Q6. (c) Reflex angle
An angle between 180° and 360° is called a reflex angle. 200° falls in this range.
Q7. (d) Height
Point, line, and circle are geometric terms. Height is a measurement, not a geometric figure.
Q8. (b) Vertex
The common starting point where two rays meet to form an angle is called the vertex.
Q9. (b) 180°
∠A + ∠B = 85° + 95° = 180°
Q10. (c) A line segment
The shortest path or distance between two points is called a line segment.
Q11.
Definition: A ray is a portion of a line that starts at one point (initial point) and extends infinitely in one direction.
Real-life examples:
1. Sun rays - start from the sun and travel in one direction
2. Beam of light from a torch - starts from the bulb and goes in one direction
3. Light from a lighthouse beam
4. Laser pointer beam
Q12.
Given: Two angles = 55° and 35°
Sum: 55° + 35° = 90°
Type: The resulting angle is a Right Angle (exactly 90°).
Q13.
Given: Ashoka Chakra has 24 spokes
Solution:
Total angle at center = 360°
Number of spokes = 24
Angle between consecutive spokes = 360° ÷ 24 = 15°
Q14.
Answer: Yes, we can have a triangle with all three angles as acute angles.
Justification: An acute angle is less than 90°.
Example: A triangle with angles 60°, 60°, and 60° (Equilateral triangle)
All three angles are less than 90°, so all are acute.
Sum = 60° + 60° + 60° = 180° ✓
Q15.
[Students should draw a quadrilateral ABCD with four points not on the same line]
Four angles formed in quadrilateral ABCD:
1. ∠DAB (or ∠BAD) - angle at vertex A
2. ∠ABC (or ∠CBA) - angle at vertex B
3. ∠BCD (or ∠DCB) - angle at vertex C
4. ∠CDA (or ∠ADC) - angle at vertex D
Q16.
Let: First angle = x
Second angle = x + 28°
Given: Angles are complementary (sum = 90°)
x + (x + 28°) = 90°
2x + 28° = 90°
2x = 90° - 28°
2x = 62°
x = 31°
Answer:
First angle = 31°
Second angle = 31° + 28° = 59°
Verification: 31° + 59° = 90° ✓
Q17.
Given: Complete angle = 360°
Ratio = 2:3:4:6
Sum of ratio parts = 2 + 3 + 4 + 6 = 15
Solution:
First part = (2/15) × 360° = 48°
Second part = (3/15) × 360° = 72°
Third part = (4/15) × 360° = 96°
Fourth part = (6/15) × 360° = 144°
Types:
• 48° - Acute angle (< 90°)
• 72° - Acute angle (< 90°)
• 96° - Obtuse angle (> 90° and < 180°)
• 144° - Obtuse angle (> 90° and < 180°)
Verification: 48° + 72° + 96° + 144° = 360° ✓
Q18.
(a) Angle Bisector:
An angle bisector is a ray that divides an angle into two equal parts (angles of equal measure).
[Students should draw an angle with its bisector]
(b) Drawing 120° angle:
[Students should use protractor to draw 120° angle]
Steps:
1. Draw a ray OA
2. Place protractor with center at O and 0° line along OA
3. Mark point B at 120°
4. Draw ray OB
5. ∠AOB = 120°
(c) Drawing angle bisector by paper folding:
1. Fold the paper so that ray OA overlaps ray OB
2. The crease formed is the angle bisector OC
3. ∠AOC = ∠COB
(d) Measuring angles after bisection:
Each angle = 120° ÷ 2 =
60°
∠AOC = 60° and ∠COB = 60°
(e) Type: Both 60° angles are
Acute angles (< 90°)
Q19. Case Study 1: Pizza Slices
(a) Angle formed by each slice:
Total angle = 360°
Number of slices = 8
Angle per slice = 360° ÷ 8 = 45°
(b) Total angle for 3 slices:
Angle = 3 × 45° = 135°
(c) Type of angle:
135° is an Obtuse angle (> 90° and < 180°)
(d) Slices needed for straight angle:
Straight angle = 180°
Number of slices = 180° ÷ 45° = 4 slices
Q20. Case Study 2: Ferris Wheel
(a) Angle between consecutive cabins:
Total angle = 360°
Number of cabins = 15
Angle = 360° ÷ 15 = 24°
(b) Angle between cabin 1 and cabin 6:
Number of gaps = 6 - 1 = 5
Angle = 5 × 24° = 120°
(c) Angle for half rotation:
Half rotation = 360° ÷ 2 = 180°
(d) Type of angle between cabin 1 and cabin 4:
Number of gaps = 4 - 1 = 3
Angle = 3 × 24° = 72°
Type: Acute angle (< 90°)