CBSE Class 6 Mathematics Lines and Angles Practice Paper Assignment Set 02 with Answers

Practice Paper 05 for CBSE Class 6 Maths Ganita Prakash Chapter 2 Lines and Angles has 20 questions worth 40 marks, arranged in Sections A to E, and every question below has a worked, step-by-step answer. This paper focuses on reading a double-scale protractor, angles around a point adding up to 360°, zero, acute, obtuse and reflex angles, clock-hand angles at 5:00 and 8:00, and the angles of a triangular flag.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Find the degree measures of ∠BXE, ∠CXE, ∠AXB and ∠BXC.

Answer:
X is the centre of the protractor, ray XE lies on the 0 of the inner scale and ray XA on the 0 of the outer scale.
Reading from XE (inner scale): ray XB is at 115° and ray XC is at 85°.
∠BXE = 115° and ∠CXE = 85°.
Reading from XA (outer scale): ray XB is at 65°, so ∠AXB = 65° (check: 180° − 115° = 65°).
∠BXC = ∠BXE − ∠CXE = 115° − 85° = 30°.
In simple words: Read each arm on the scale that starts at 0 on the other arm: 115°, 85°, 65° and 30°.

Teacher's Note:
1. Pick the scale whose 0 lies on one arm of the angle.
2. An angle between two slanting rays is a difference of readings.

Question 12. Find the missing angle if three angles around a point are 110°, 95°, and 45°.
Answer:
Angles around a point add up to 360°.
Sum of the given angles = 110° + 95° + 45° = 250°.
Missing angle = 360° − 250° = 110°.
In simple words: Take the three angles away from 360° to get 110°.

Teacher's Note:
1. Add the known angles first, then subtract from 360°.
2. Check that all four angles total 360°.

Question 13. Classify the angle formed between the hands of a clock at 5:00.
Answer:
Each hour gap on a clock is 360° ÷ 12 = 30°.
At 5:00 the minute hand is at 12 and the hour hand at 5, which is 5 gaps away.
Angle = 5 × 30° = 150°.
150° is more than 90° but less than 180°, so it is an obtuse angle.
In simple words: At 5:00 the hands make 150°, which is obtuse.

Teacher's Note:
1. Use the smaller angle between the hands.
2. The other side of the hands makes the reflex angle 210°.

Question 14. A circular clock face is divided into 24 equal parts for a 24-hour clock design. The designer wants to calculate the angle between two consecutive marks. Calculate the angle between two adjacent marks.
Answer:
One complete turn around the clock face is 360°.
It is shared equally by 24 parts.
Angle between two adjacent marks = 360° ÷ 24 = 15°.
In simple words: Share 360° equally among 24 marks: 15° each.

Teacher's Note:
1. Equal parts of a full turn: divide 360°.
2. A normal 12-hour clock gives 30° per mark.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Use a protractor to draw angles having the following degree measures:
(a) 110°, (b) 40°, (c) 75°
Answer:
For each angle: draw a ray, place the protractor's centre on its starting point with the base along the ray, mark the required reading on the scale that starts at 0 on the ray, and join the mark to the vertex.
(a) 110° is obtuse, so the second arm leans back past the upright.
(b) 40° is acute, a narrow opening.
(c) 75° is acute but close to a right angle.

In simple words: Mark 110°, 40° and 75° from the 0 on each base ray and join to the vertex.

Teacher's Note:
1. Guess the type of angle before drawing, to catch scale mistakes.
2. Keep the protractor's centre exactly on the vertex.

Question 16. Find the angle between the hands of a clock at 8:00 and classify it.
Answer:
Each hour gap is 30°. At 8:00 the minute hand is at 12 and the hour hand is at 8.
Going the short way, from 8 to 12 there are 4 gaps: 4 × 30° = 120°.

120° lies between 90° and 180°, so it is an obtuse angle.
(Going the long way round, from 12 to 8, the hands make 8 × 30° = 240°, which is a reflex angle.)
In simple words: At 8:00 the hands make 120° (obtuse), or 240° the other way round (reflex).

Teacher's Note:
1. Count the gaps the short way round.
2. The two angles between the hands always add up to 360°.

Question 17. Three angles around a point measure 100°, 85°, and 95°. Find the fourth angle and classify it.
Answer:
Angles around a point add up to 360°.
Sum of the given angles = 100° + 85° + 95° = 280°.
Fourth angle = 360° − 280° = 80°.
80° is less than 90°, so it is an acute angle.
In simple words: The fourth angle is 360° − 280° = 80°, which is acute.

Teacher's Note:
1. A full turn is 360°.
2. Compare the answer with 90° to classify it.

Section D: Long Answer Question (5 Marks)

Question 18. During a science exhibition, a student uses a protractor to measure angles formed by rays originating from a point. She measures two angles as 135° and 75°. She wonders what the third angle would be if these three rays divide the circle into three parts. Calculate the third angle formed by the rays and classify all three angles.
Answer:
The three angles between the rays together make a complete turn, so they add up to 360°.
Sum of the known angles = 135° + 75° = 210°.
Third angle = 360° − 210° = 150°.

Classification:
135°: between 90° and 180°, so obtuse.
75°: less than 90°, so acute.
150°: between 90° and 180°, so obtuse.
Check: 135° + 75° + 150° = 360°.
In simple words: The third angle is 150°; 135° and 150° are obtuse and 75° is acute.

Teacher's Note:
1. Three rays from a point split the full turn into three angles.
2. Always add the three angles to check for 360°.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Story – The Triangular Flag
Riya is helping her school organize the annual sports day. She has been asked to design a triangular flag that will be used to mark the finish line for the races. While drawing the flag, she notes that two of its angles measure 70° and 55°. Curious to understand more about her design, she decides to find out the third angle of the flag, classify all three angles, and verify if their sum matches the properties of a triangle.
(i) Find the third angle.
(ii) Classify all three angles.
(iii) Verify the total of the angles.
Answer:
(i) The angles of a triangle add up to 180°. Third angle = 180° − (70° + 55°) = 180° − 125° = 55°.

(ii) 70°, 55° and 55° are all less than 90°, so all three are acute angles (the flag is an acute-angled triangle; with two equal angles it is also isosceles).
(iii) 70° + 55° + 55° = 180°, which matches the angle sum property of a triangle.
In simple words: The third angle is 55°, all three angles are acute, and together they make 180°.

Teacher's Note:
1. Subtract the two known angles from 180°.
2. Two equal angles mean two equal sides.

Question 20. Story – The Stage Lights
During the annual school play, the stage crew is setting up four spotlights arranged in a circle around the center of the stage. The angles formed between the lights are 85°, 95°, and 110°. To complete the setup perfectly, the crew needs to find the fourth angle, classify all four angles based on their measures, and check if the total of all the angles matches the expected full rotation around a point.
(i) Find the fourth angle.
(ii) Classify all four angles.
(iii) Verify the total.
Answer:
(i) Angles all the way around the centre make a full turn of 360°. Fourth angle = 360° − (85° + 95° + 110°) = 360° − 290° = 70°.

(ii) 85° and 70° are less than 90°, so they are acute; 95° and 110° are between 90° and 180°, so they are obtuse.
(iii) 85° + 95° + 110° + 70° = 360°, one full rotation around the centre.
In simple words: The fourth angle is 70°; two angles are acute, two are obtuse, and all four make 360°.

Teacher's Note:
1. Around a point, the total is always 360°.
2. Classify each angle by comparing with 90°.