CBSE Class 6 Mathematics Lines and Angles Worksheet Set 01

Very Short Answer Questions

Question 1. What does a point show? State whether a point has any length or breadth.
Answer:
A point shows a precise location. It has no length, no breadth (and no height).

Teacher's Note:
1. A point is only a position.
2. The dot we draw just helps us see it.

Question 2. Write any two things from daily life that give the idea of a point.
Answer:
The sharpened tip of a pencil and the pointed end of a needle. (The tip of a compass is another example.)

Teacher's Note:
1. Look for very sharp tips.
2. Any fine tip gives the idea of a point.

Question 3. Define a line segment. How is the line segment joining the points S and T written?
Answer:
A line segment is the shortest path joining two points, including the two end points.
It is written as \( \overline{ST} \) or \( \overline{TS} \).

Teacher's Note:
1. The order of the letters does not matter for a segment.
2. A segment has a fixed length.

Question 4. How many end points does a line have? Can its whole picture be drawn on paper?
Answer:
A line has no end points. Its whole picture cannot be drawn, because it goes on endlessly in both directions.

Teacher's Note:
1. We draw only a part of a line, with arrows at both ends.
2. The arrows show it never stops.

Question 5. Define a ray and give one everyday model of a ray.
Answer:
A ray is a part of a line that starts at one point and goes on endlessly in one direction.
Example: a beam of light from a torch.

Teacher's Note:
1. A ray has one starting point.
2. Sun rays and lighthouse beams are also models.

Question 6. Name the two parts of an angle.
Answer:
The vertex (the common starting point) and the two arms (the two rays forming the angle).

Teacher's Note:
1. Vertex is the corner.
2. Arms are the two rays.

Question 7. Two rays \( \overrightarrow{OP} \) and \( \overrightarrow{OM} \) form an angle. Write two names for this angle using the symbol ∠.
Answer:
∠POM and ∠MOP. In both, the vertex O is in the middle.

Teacher's Note:
1. Vertex letter goes in the middle.
2. Either arm point can come first.

Question 8. What is a straight angle? How much of a full turn is it?
Answer:
A straight angle is an angle whose two arms lie in one straight line.
It is a half turn, that is 180°.

Teacher's Note:
1. Straight angle = half turn = 180°.
2. Its arms point in opposite directions.

Question 9. Write the measure of a right angle. Which capital letter does a right angle look like?
Answer:
A right angle measures 90°. It looks like the capital letter L.

Teacher's Note:
1. A right angle is a quarter turn.
2. Book corners are right angles.

Question 10. How many degrees are there in one full turn?
Answer:
One full turn measures 360°, as it is divided into 360 equal parts of 1° each.

Teacher's Note:
1. 360° is the full circle.
2. Half of it is 180°, a quarter is 90°.

Question 11. Between which two measures does an acute angle lie?
Answer:
An acute angle is more than 0° and less than 90°, that is, smaller than a right angle.

Teacher's Note:
1. Acute means sharp.
2. 90° itself is not acute.

Question 12. While placing one angle over another to compare them, what must be made to overlap first?
Answer:
The vertices of the two angles must overlap first; then one arm of each is placed along the other.

Teacher's Note:
1. Vertex on vertex first.
2. Then compare the second arms.

Question 13. Which of the two can be measured with a ruler, a line segment or a line? Give the reason.
Answer:
A line segment, because it has two end points and so a fixed length.
A line has no end points, so its length cannot be measured.

Teacher's Note:
1. Only something with two ends has a length.
2. A line never ends.

Question 14. Can the ray \( \overrightarrow{AB} \) also be written as \( \overrightarrow{BA} \)? Give a reason for your answer.
Answer:
No. \( \overrightarrow{AB} \) starts at A, while \( \overrightarrow{BA} \) starts at B, so the two rays go in opposite directions.

Teacher's Note:
1. In a ray the first letter is the starting point.
2. Order matters for rays, not for segments.

Question 15. Three rays \( \overrightarrow{QX} \), \( \overrightarrow{QY} \) and \( \overrightarrow{QZ} \) start from the point Q. Why can the angle between \( \overrightarrow{QX} \) and \( \overrightarrow{QY} \) not be named simply as ∠Q?
Answer:
Three angles share the vertex Q, so ∠Q does not tell which two rays are meant.
It must be named with a point from each arm: ∠XQY.

Teacher's Note:
1. Use three letters when rays share a vertex.
2. The vertex stays in the middle.

Question 16. Ravi opens a pair of scissors and Mira opens a much longer pair of scissors by the same amount of turn. Whose blades make the greater angle? Why?
Answer:
Both angles are equal. The size of an angle depends only on the amount of turn about the vertex, not on the length of the blades.

Teacher's Note:
1. Longer arms do not make a bigger angle.
2. Same turn, same angle.

Question 17. A pair of rotating arms is placed over an angle-shaped slit in a cardboard. State the condition under which the arms will pass through the slit.
Answer:
The arms pass through only when the angle between them is exactly equal to the angle of the slit, whatever the length of the arms.

Teacher's Note:
1. The slit checks only the angle.
2. Bigger or smaller openings get stuck.

Question 18. What name is given to two lines that meet each other at right angles?
Answer:
They are called perpendicular lines.

Teacher's Note:
1. Perpendicular means meeting at 90°.
2. The edges of a page corner are perpendicular.

Question 19. Give one reason why 360 was found to be a useful number of equal parts for a full turn.
Answer:
360 can be divided exactly by many small numbers such as 2, 3, 4, 5, 6, 8, 9, 10, 12 and 24, so a circle can be split into equal parts with whole-number degrees.

Teacher's Note:
1. Try dividing 360 by small numbers.
2. Many give whole answers.

Question 20. What is meant by the angle bisector of an angle?
Answer:
It is the line through the vertex that divides the angle into two equal angles, like the crease formed when an angle is folded in half.

Teacher's Note:
1. Bisect means cut into two equal parts.
2. Folding arm on arm gives the bisector.

Question 21. Find the angle between the hour hand and the minute hand of a clock at 5 o’clock.
Answer:
Each hour gap is 360° ÷ 12 = 30°. At 5 o’clock the hands are 5 gaps apart.
Angle = 5 × 30° = 150°.

Teacher's Note:
1. Count the hour gaps between the hands.
2. 150° is obtuse.

Question 22. Write the first two steps you would follow to draw ∠ABC = 70° with a protractor.
Answer:
Step 1: Draw the base arm \( \overrightarrow{BC} \).
Step 2: Place the centre of the protractor on the vertex B and line up \( \overrightarrow{BC} \) with the 0° line.

Teacher's Note:
1. The vertex is the middle letter, B.
2. Start counting from the 0 on the base arm.

Question 23. A ray divides a straight angle into two equal angles. Write the measure of each angle and the name given to such an angle.
Answer:
Each part = 180° ÷ 2 = 90°. Such an angle is called a right angle.

Teacher's Note:
1. Half a straight angle is a right angle.
2. The ray is perpendicular to the line.

Question 24. Classify each of these angles as acute, right, obtuse, straight or reflex: 95° and 185°.
Answer:
95° is between 90° and 180°, so it is obtuse.
185° is between 180° and 360°, so it is reflex.

Teacher's Note:
1. Compare with 90° and 180°.
2. Just past 180° is already reflex.

Question 25. A full turn is divided into 9 equal parts. Find the measure of each part.
Answer:
Each part = 360° ÷ 9 = 40°, an acute angle.

Teacher's Note:
1. Divide 360 by the number of parts.
2. Check: 9 × 40 = 360.

Question 26. The Ashoka Chakra has 24 equally spaced spokes. Find the largest acute angle formed between two of its spokes.
Answer:
Neighbouring spokes make 360° ÷ 24 = 15°. Angles between spokes are 15°, 30°, 45°, 60°, 75°, 90°, …
Six gaps give 90°, which is not acute, so the largest acute angle is 5 × 15° = 75°.

Teacher's Note:
1. List multiples of 15° up to 90°.
2. 90° is right, not acute.

Question 27. At a vertex, the reflex angle between two rays measures 290°. Find the other angle at the same vertex and write its type.
Answer:
The two angles make one full turn, so the other angle = 360° − 290° = 70°.
70° is less than 90°, so it is an acute angle.

Teacher's Note:
1. The two angles at a vertex add up to 360°.
2. Then classify the answer.

Question 28. Your geometry box has only a semicircular protractor marked up to 180°. Explain in one or two lines how you would use it to draw an angle of 240°.
Answer:
Since 360° − 240° = 120°, draw an angle of 120° with the protractor.
The angle on the other side of the arms, marked with a curve, is then 240°.

Teacher's Note:
1. Draw the smaller angle and mark the reflex side.
2. The two sides add up to 360°.

Question 29. The measure of an angle is 48°. It is doubled, and the answer is doubled once more. What type of angle do you get at the end?
Answer:
2 × 48° = 96°, then 2 × 96° = 192°.
192° is more than 180° and less than 360°, so it is a reflex angle.

Teacher's Note:
1. Do the two doublings one by one.
2. 96° is only the middle step.

Question 30. Three points A, B and C are marked on a sheet so that they do not lie on one line. How many lines pass through pairs of these points, and how many angles can be named using A, B and C?
Answer:
Three lines: \( \overleftrightarrow{AB} \), \( \overleftrightarrow{BC} \) and \( \overleftrightarrow{CA} \).
Three angles: ∠ABC, ∠BCA and ∠CAB.

Teacher's Note:
1. Each pair of points gives one line.
2. Each point can be a vertex once.