| 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. The measure of a complete angle is:
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Q2. Two lines that meet at right angles are called:
(a) Parallel lines
(b) Perpendicular lines
(c) Intersecting lines
(d) Concurrent lines
Q3. The angle formed by ⅜ of a complete rotation is:
(a) 90°
(b) 135°
(c) 180°
(d) 270°
Q4. An angle of 91° is classified as:
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Reflex angle
Q5. How many acute angles can a triangle have at most?
(a) One
(b) Two
(c) Three
(d) Four
Q6. The sum of angles around a point is:
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Q7. If two angles are complementary and one angle is 36°, the other angle is:
(a) 44°
(b) 54°
(c) 64°
(d) 144°
Q8. The angle between the hour and minute hands at 2 o'clock is:
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Q9. Which of the following is an example of an obtuse angle?
(a) 45°
(b) 90°
(c) 110°
(d) 180°
Q10. A ray OA can also be written as:
(a) AO
(b) OA only
(c) Both OA and AO
(d) None of these
Q11. Define complementary angles. Give an example with proper angle measures.
Q12. Draw a line segment PQ of length 6 cm. Mark a point R on it such that PR = 4 cm. What is the length of RQ?
Q13. Three angles of measure 70°, 80°, and x° together form a straight angle. Find the value of x.
Q14. Can two obtuse angles be supplementary? Justify your answer with reasoning.
Q15. The sum of three angles is 180°. If the angles are in the ratio 2:3:4, find each angle. What can you say about the sum?
Q16. An angle is 20° more than twice its complement. Find the angle and its complement.
Q17. From a point O, five rays OA, OB, OC, OD, and OE are drawn. If ∠AOB = 30°, ∠BOC = 40°, ∠COD = 35°, and ∠DOE = 45°, find ∠AOE.
Q18. (a) Draw a circle of radius 5 cm. Mark its center as O.
(b) Draw two radii OA and OB such that ∠AOB = 72°.
(c) Using paper folding or compass, divide ∠AOB into two equal parts.
(d) Find ∠AOC and ∠BOC by measurement.
(e) Verify that ∠AOC = ∠BOC = ∠AOB ÷ 2.
Q19. Case Study 1: Bicycle WheelA bicycle wheel has 18 equally spaced spokes connecting the rim to the hub at the center.
Based on the above information, answer the following:
(a) What is the angle between two adjacent spokes at the center? (1 mark)
(b) What is the angle between the 1st spoke and the 7th spoke? (1 mark)
(c) How many spokes are between angles measuring exactly 180°? (1 mark)
(d) What type of angle is formed between the 1st and 10th spoke? (1 mark)
Q20. Case Study 2: Street Light AnglesAt a crossroad, five streets meet at a point. The angles between consecutive streets are 55°, 70°, 85°, 75°, and x°.
Based on the above information, answer the following:
(a) What is the sum of all angles at the crossroad? (1 mark)
(b) Find the value of x. (1 mark)
(c) Which angles are acute and which are obtuse? (1 mark)
(d) If a car turns from the first street to the third street, through what total angle does it turn? (1 mark)
NOTE: For the complete version with detailed answer keys, please refer to the full HTML code provided in the conversation. This preview version contains all questions. The complete answer key with step-by-step solutions will be added when you copy the full HTML code from the chat.