CBSE Class 6 Mathematics Lines and Angles MCQs Set 11

Answer: (a) a precise location

Explanation:
1. A point only shows an exact position on the paper.
2. It has no length, no breadth and no height, so (b), (c) and (d) cannot be right.
3. So a point stands for a precise location.

Teacher's Note:
1. A dot is only a picture of a point.
2. The real point is imagined to be invisibly thin.

Answer: (c) the line segment AB

Explanation:
1. The shortest path from A to B, including both points, is the line segment AB.
2. A ray and a line go on endlessly, so neither can be a shortest path.
3. So the answer is the line segment AB.

Teacher's Note:
1. A line segment starts and stops at its two end points.
2. Think of a tight thread stretched between two pins.

Answer: (d) It has no end points and goes on endlessly in both directions.

Explanation:
1. A line is a line segment extended without end on both sides.
2. So it has no end points, and its length cannot be measured.
3. Two end points belong to a segment and one end point to a ray, so the answer is (d).

Teacher's Note:
1. Segment: 2 end points; ray: 1; line: 0.
2. Arrows on both sides of the symbol show that a line never ends.

Answer: (b) \( \overrightarrow{DP} \)

Explanation:
1. A ray is written with a single arrow over the two letters, with the starting point written first.
2. So the ray is \( \overrightarrow{DP} \).
3. A bar means a segment and a double arrow means a line, so the answer is (b).

Teacher's Note:
1. Bar: segment; double arrow: line; single arrow: ray.
2. The starting point always comes first in a ray.

Answer: (c) O

Explanation:
1. In the name of an angle, the vertex letter is always the middle letter.
2. In ∠POM the middle letter is O, so O is the vertex.
3. P and M are points on the two arms.

Teacher's Note:
1. Vertex in the middle, arm points on the sides.
2. ∠POM and ∠MOP are the same angle.

Answer: (d) 360°

Explanation:
1. A full turn is divided into 360 equal parts, each of 1°.
2. So one full turn measures 360°.
3. A quarter turn is 90° and a half turn is 180°.

Teacher's Note:
1. Learn 90°, 180°, 360° as quarter, half and full turns.
2. 270° is three-quarters of a turn.

Answer: (b) two right angles

Explanation:
1. A right angle is half of a straight angle.
2. In degrees, 180° ÷ 90° = 2.
3. So a straight angle contains two right angles.

Teacher's Note:
1. Four right angles make a full turn.
2. Two right angles make a straight angle.

Answer: (d) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. 65° is less than 90°, so it is acute (r). 90° is a right angle (s).
2. 115° is between 90° and 180°, so it is obtuse (p). 300° is between 180° and 360°, so it is reflex (q).
3. So the match is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. Compare each measure with 90°, 180° and 360°.
2. Match the easy one (90°) first.

Answer: (a) an acute angle

Explanation:
1. The opening between \( \overrightarrow{BA} \) and \( \overrightarrow{BC} \) is clearly smaller than the corner of a page.
2. So ∠ABC is less than 90°.
3. An angle smaller than a right angle is an acute angle.

Teacher's Note:
1. Use the corner of a page as a right-angle tester.
2. Smaller than the corner means acute.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A is true: a line goes on endlessly both ways, so it has no end points.
2. R is true: it is the meaning of a line segment.
3. But R talks about a segment being the shortest path, which does not explain why a line has no end points. So R is not the correct explanation of A.

Teacher's Note:
1. Two true facts need not be linked.
2. Ask whether R answers 'why A?'.

Answer: (a) Only Statement I is true.

Explanation:
1. Two points fix exactly one line, so Statement I is true.
2. Through one point we can draw countless lines in all directions, so Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. Try it: draw many lines through one dot.
2. With two dots, only one straight line fits.

Answer: (c) 60°

Explanation:
1. The 12 hour marks divide 360° into 12 equal gaps of 360° ÷ 12 = 30°.
2. At 2 o’clock the hands are 2 gaps apart.
3. So the angle is 2 × 30° = 60°.

Teacher's Note:
1. Each hour gap on a clock is 30°.
2. Count the gaps between the two hands.

Answer: (d) so that an angle can be read whichever arm is placed along the 0° mark

Explanation:
1. One scale rises from left to right and the other from right to left.
2. So we can start from 0° on the right or on the left.
3. This lets us read an angle whichever arm is placed along the 0° mark.

Teacher's Note:
1. Always read the scale whose 0 lies on the base arm.
2. Both scales are in degrees.

Answer: (b) the vertices of the two angles fall on each other

Explanation:
1. In superimposition one angle is placed over the other.
2. The vertices must fall on each other and one arm of each must lie together.
3. Arm length and colour do not affect the size of an angle, so the answer is (b).

Teacher's Note:
1. Vertex on vertex, arm on arm.
2. Then look at where the second arms fall.

Answer: (c) 115°

Explanation:
1. A straight angle measures 180°.
2. The ray \( \overrightarrow{OC} \) splits it into ∠AOC and ∠COB, so the two add up to 180°.
3. ∠COB = 180° − 65° = 115°.

Teacher's Note:
1. The two parts of a straight angle add up to 180°.
2. 25° would be the answer for a right angle, a common trap.

Answer: (a) 140°

Explanation:
1. L, O, M are on one straight line, so ∠LOM is a straight angle of 180°.
2. ∠LON + ∠NOM = 180°, that is x + 40° = 180°.
3. So x = 180° − 40° = 140°.

Teacher's Note:
1. Angles on one side of a straight line add up to 180°.
2. x is obtuse, so 50° cannot be right.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. R is true: this is the meaning of the size of an angle.
2. Drawing the arms longer adds no turning, so the size stays the same. A is true.
3. R gives the reason for A, so R is the correct explanation.

Teacher's Note:
1. Angle size is about turning, not length.
2. Here R really answers 'why A?'.

Answer: (b) Only Statement II is true.

Explanation:
1. An obtuse angle must be less than 180°, not 360°, so Statement I is false.
2. Statement II gives the correct range of an acute angle, so it is true.
3. So only Statement II is true.

Teacher's Note:
1. Obtuse: between 90° and 180°.
2. Angles between 180° and 360° are reflex.

Answer: (a) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. A bar means a line segment (r), and a double arrow means a line (s).
2. A single arrow means a ray (p), and the sign ∠ means an angle (q).
3. So the match is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. The marks on top tell how the figure ends.
2. No arrow: stops; one arrow: one endless side; two arrows: both.

Answer: (b) Only Statement II is true.

Explanation:
1. 360° ÷ 5 = 72°, not 60°, so Statement I is false.
2. 360° ÷ 8 = 45°, so Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. 60° parts would need 6 equal parts.
2. Divide 360 by the number of parts.

Answer: (d) A is false, but R is true.

Explanation:
1. A bisector always cuts an angle into two equal parts, so A is false.
2. Folding one arm onto the other makes two parts that match exactly, so they are equal. R is true.
3. So A is false but R is true.

Teacher's Note:
1. 'Bi-sect' means cut into two equal parts.
2. The fold crease is the angle bisector.

Answer: (c) 90°

Explanation:
1. The ray \( \overrightarrow{OQ} \) lies between \( \overrightarrow{OP} \) and \( \overrightarrow{OR} \).
2. So ∠POR = ∠POQ + ∠QOR = 40° + 50°.
3. ∠POR = 90°.

Teacher's Note:
1. When a ray lies inside an angle, the two parts add up.
2. 10° is the difference, a common trap.

Answer: (c) A is true, but R is false.

Explanation:
1. A describes the correct first steps of drawing an angle with a protractor, so A is true.
2. The same protractor is used both to measure and to draw angles, so R is false.
3. So A is true but R is false.

Teacher's Note:
1. A protractor measures and draws.
2. Watch for words like 'only' and 'never'.

Answer: (d) 15°

Explanation:
1. The 24 spokes divide one full turn into 24 equal angles.
2. Each angle is 360° ÷ 24.
3. So the angle is 15°.

Teacher's Note:
1. Equal spokes share 360° equally.
2. Check: 24 × 15 = 360.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The arms slip through only when their opening matches the opening of the slit, so A is true.
2. This depends on the angle alone, not on how long the arms are, so R is true.
3. Since passing through depends only on the angle, the angles must be equal; R explains A.

Teacher's Note:
1. The slit tests the angle, not the length.
2. Long or short arms both pass if the angle matches.

Answer: (d) Neither statement is true.

Explanation:
1. A reflex angle must be more than 180°; exactly 180° is a straight angle. Statement I is false.
2. An angle such as 200° is greater than 90° but it is reflex, not obtuse. Statement II is false.
3. So neither statement is true.

Teacher's Note:
1. Obtuse has an upper limit: 180°.
2. One counterexample is enough to reject 'any'.

Answer: (c) 21°

Explanation:
1. For 21°: 42°, 63° and 84° are all acute, and 5 × 21° = 105° is obtuse. This fits.
2. For 15°: 5 × 15° = 75° is still acute. For 18°: 5 × 18° = 90° is a right angle, not obtuse.
3. For 24°: 4 × 24° = 96° is already not acute. So the answer is 21°.

Teacher's Note:
1. Test each option against every condition.
2. A right angle is neither acute nor obtuse.

Answer: (b) 250°

Explanation:
1. The two angles at O together make one full turn of 360°.
2. The dashed curve goes the long way round, so x is the reflex angle.
3. x = 360° − 110° = 250°.

Teacher's Note:
1. Reflex angle = 360° − the smaller angle.
2. Look at which way the curve goes round.

Answer: (d) A is false, but R is true.

Explanation:
1. At 9 o’clock the hands are 3 hour gaps apart, so the smaller angle is 3 × 30° = 90°. 270° is the reflex angle. A is false.
2. 360° ÷ 12 = 30°, so R is true.
3. So A is false but R is true.

Teacher's Note:
1. 'Smaller angle' is never more than 180°.
2. Count gaps the short way round.

Answer: (a) (i)-(s), (ii)-(p), (iii)-(q), (iv)-(r)

Explanation:
1. One-third of 360° is 120° (s); three-quarters of 360° is 270° (p).
2. One-eighth of 360° is 45° (q); two-thirds of 360° is 240° (r).
3. So the match is (i)-(s), (ii)-(p), (iii)-(q), (iv)-(r).

Teacher's Note:
1. Find the part first, then multiply: 360 ÷ 3 = 120, so two-thirds is 240.
2. Quarter turn = 90°, so three-quarters = 270°.