Regular revision with Class 6 Maths MCQ with Answers and Ganita Prakash Class 6 Maths Chapter 2 Lines and Angles MCQ improves accuracy in objective exams.
MCQ on Lines and Angles Class 6
Lines and Angles MCQ Class 6
Class 6 Maths Lines and Angles MCQ
Question 1.
A line segment has:
(a) No endpoint
(b) One endpoint
(c) Two endpoints
(d) Infinite endpoints
Solution:
(c) Two endpoints
We know that the shortest path from point A to point B (including A and B) is called the line segment AB. It is denoted by either \(\overline{A B}\) or \(\overline{B A}\). The points A and B are called the endpoints of the line segment \(\overline{A B}\).
Question 2.
Which of these represents a ray in real life?
(a) Beam of light from a torch
(b) A thread
(c) A compass needle
(d) A pencil
Solution:
(a) Beam of light from a torch
We know that in geometry, a ray starts at one point and goes on infinitely in one direction.
The light comes out from the head of the torch and travels in a straight line. This is like a ray in real life.
A thread has two ends. In geometry, this is more like a line segment, not a ray.
A compass needle rotates and points in a direction, but it has two ends, and it does not extend infinitely. It’s not fixed in one direction from one point.
A pencil is a physical object with two definite ends. lake a thread, it is a line segment, not a ray.
Question 3.
The shortest path between two points is:
(a) A ray
(b) A line segment
(c) A curve
(d) A line
Solution:
(b) A line segment
We know that the shortest path between two points (including both points) is called a line segment.
Question 4.
Can you draw a complete line on paper?
(a) Yes, only if the line is horizontal
(b) Yes, only if the line is vertical
(c) No
(d) Can’t say
Solution:
(c) No
We know that a line passing through two points A and B is written as \(\overleftrightarrow{A B}\). It extends infinitely in both directions. Therefore, a complete line cannot be drawn on paper.
Question 5.
An angle is formed by two:
(a) Points
(b) Rays with different starting points
(c) Rays with a common starting point
(d) Line segments
Solution:
(c) Rays with a common starting point
We know that an angle is formed by two rays having a common starting point.
Question 6.
Which of the following does not show angle formation by rotation?
(a) Opening a book
(b) Drawing a straight line
(c) Turning the hands of a clock
(d) Opening a pair of scissors
Solution:
(b) Drawing a straight line
Opening a book: Yes, it makes an angle between the two covers.
Drawing a straight line: No turning or rotation happens. It’s just a line.
Turning the hands of a clock: Yes, the hands rotate and form angles.
Opening a pair of scissors: Yes, the blades form an angle when opened.
Question 7.
Superimposition of angles means:
(a) Extending both arms
(b) Placing one angle over the other
(c) Comparing only vertices
(d) Measuring angles with a ruler
Solution:
(b) Placing one angle over the other
The word superimpose means to place one thing exactly on top of another so that you can compare them. So, superimposition of angles means placing one angle over another angle so that their vertices (corners) and one arm (side) coincide.
This helps us see whether the two angles are equal or not, without using a protractor.
Question 8.
In ∠POM, what is the vertex of the angle?
(a) P
(b) M
(c) O
(d) PO
Solution:
(c) O
In ∠POM, 0 is the vertex of the angle as it is written in the middle.
Question 9.
Superimposed angles are equal when:
(a) They look similar
(b) Their vertices match but arms don’t
(c) Both rays and vertex match exactly
(d) They are on the same side
Solution:
(c) Both rays and vertex match exactly
We know that when two angles are superimposed, and the common vertex and the two rays of both angles lie on each other, then the sizes of the angles are equal.
Question 10.
An angle greater than 90° but less than 180° is called:
(a) Right angle
(b) Acute angle
(c) Reflex angle
(d) Obtuse angle
Solution:
(d) Obtuse angle
We know that an angle greater than 90° but less than 180° is called obtuse angle.
Question 11.
An angle that measures exactly 180° is called a:
(a) Right angle
(b) Reflex angle
(c) Obtuse angle
(d) Straight angle
Solution:
(d) Straight angle
An angle that measures exactly 180° is called a straight angle.
Question 12.
Which of the following is a reflex angle?
(a) 85°
(b) 135°
(c) 180°
(d) 220°
Solution:
(d) 220°
An angle that is greater than 180° but less than 360° is known as a reflex angle. Thus, 220° is a reflex angle.
Question 13.
The markings, formed by repeated folding of a semi-circle, divide it into equal parts using the concept of:
(a) Angle scaling
(b) Rotation
(c) Angle bisector
(d) Circular radius
Solution:
(c) Angle bisector
When we fold a semi-circle repeatedly, each fold divides the angle into two equal parts. This is done using the concept of an angle bisector, which divides the angle into two equal halves.
Question 14.
What is the measure of the angle between the hour hand and the minute hand of a clock when it is 4 o’clock?
(a) 180°
(b) 120°
(c) 90°
(d) 60°
Solution:
(b) 120°
We know that the clock has 12 hours and a full circle is 360°.
So, each hour mark is \(\frac{360^{\circ}}{12}\) = 30 apart.
Thus, the angle increases by 30° for each hour.
At 4 o’clock, the hour hand is at 4 and the minute hand is at 12.
From the figure, we can see that there is a gap of 4 hour marks between the hour hand and the minute hand.
Therefore, angle between the hour hand and the minute hand at 4 o’clock = 4 × 30° = 120°
Question 15.
If there are 18 spokes in a motorcycle wheel, then the angle between two adjacent spokes is:
(a) 10°
(b) 12°
(c) 18°
(d) 20°
Solution:
(d) 20°
We know that a complete angle is equal to 360°. Given, there are 18 spokes in a motorcycle wheel.
Therefore, these 18 spokes divide the complete angle into 18 equal parts.
Thus, the angle between two adjacent spokes = \(\frac{360^{\circ}}{18}\) = 20°
Question 16.
Which of the following statements are true?
(i) A line segment has two endpoints.
(ii) A ray extends endlessly in both directions.
(iii) A line can be named using any two points on it.
(iv) A ray has one endpoint and goes on endlessly in one direction.
Choose the correct option from the following:
(a) Only (i) and (iv)
(b) Only (i) and (ii)
(c) (i), (ii) and (iii)
(d) (i), (iii) and (iv)
Solution:
(d) (i), (iii) and (iv)
We know that
A line segment has two endpoints.
A line is named using any two points that lie on the line.
A ray has one endpoint and extends in one direction.
Thus, the statements (i), (iii) and (iv) are correct.
Question 17.
Which of the following are correct ways to name a given angle?
(i) ∠XYZ
(ii) ∠ZXY
(iii) ∠X
(iv) ∠YXZ
Choose the correct option from the following:
(a) Only (i) and (ii)
(b) Only (ii) and (iii)
(c) Only (iii) and (iv)
(d) (ii), (iiii) and (iv)
Solution:
(d) (ii), (iiii) and (iv)
To name an angle, we write the letter of one arm, followed by the letter of the vertex (always in the middle), and then the letter of the other arm.
For example, if O is the vertex and OA and OB are the arms or sides of the angle, then it can be written as ∠AOB or ∠BOA. If there is no other angle formed at the same vertex, we may simply name it ∠O.
Therefore, the given angle can be written as ∠YXZ, ∠ZXY or ∠X.
Thus, (ii), (iii) and (iv) are correct ways of writing the given angle.
Question 18.
While measuring an angle using a protractor, which of the following steps are correct?
(i) Place centre of protractor on the vertex of the angle.
(ii) Align one arm with the 0° mark.
(iii) Always use the outer scale.
(iv) Use subtraction if arms fall on different marks.
Choose the correct option from the following:
(a) Only (i) and (ii)
(b) (i), (ii) and (iv)
(c) Only (iii) and (iv)
(d) (ii), (iii) and (iv)
Solution:
(b) (i), (ii) and (iv)
While measuring an angle using a protractor, place the centre of the protractor on the vertex of the angle and align one arm with the 0° mark.
Now, depending on the orientation of the given angle, either the inner or outer scale of the protractor can he used.
If neither arm lies on the 0° mark, then subtraction can help to determine the actual measurement.
Thus, (i), (ii) and (iv) are correct.
Lines and Angles Class 6 Assertion and Reason Questions
The following questions are Assertion and Reason based questions. Two statements are given, one labelled .as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Question 1.
(A): Any two points determine a unique line.
(R): Through two distinct points, only one line can be drawn.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
Through two distinct points, only one line can be drawn.
So, any two points determine a unique line.
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 2.
(A): An angle is formed when two rays have a common starting point.
(R): The two rays are called the arms of the angle and the common point is called the vertex.
Solution:
(b) Both A and R are true but R is not the correct explanation of A.
We know that an angle is formed by two rays having a common starting point.
Here is an angle formed by rays \(\overrightarrow{O P} \text { and } \overrightarrow{O M}\) where O is the common starting point.
The point 0 is called the vertex of the angle, and the rays \(\overrightarrow{O P} \text { and } \overrightarrow{O M}\) are called the arms of the angle.
Thus, both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
Question 3.
(A): Superimposition helps us to compare the size of two angles accurately.
(R): By placing one angle over another with the same vertex, we can directly compare their
opening.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
The word superimpose means to place one thing exactly on top of another so that you can compare them.
So, superimposition of angles means placing one angle over another angle so that their vertices (corners) and one arm (side) coincide.
This helps us to compare the size of two angles accurately.
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 4.
(A): Folding a semi-circle twice gives an angle of 90°.
(R): Each fold halves the angle, allowing us to mark standard angles like 45°, 90°, and 135°.
Solution:
(d) A is false but R is true.
We know that a semi-circle is half of a full circle, which is 180°. If we fold the semi-circle into 2 equal parts, each part is 90°, and if we fold it again, we get 45°. So, each fold halves the angle, allowing us to mark standard angles like 45°, 90°, and 135°.
Thus, Assertion (A) is false, but Reason (R) is true.
Question 5.
(A): The angle between the hands of a clock at 3 o’clock is 90°.
(R): Each hour mark on a clock corresponds to a 30° rotation.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know that the clock has 12 hours and a full circle is 360°.
So, each hour mark is \(\frac{360^{\circ}}{12}\) = 30° apart.
Thus, the angle increases by 30° for each hour.
At 3 o’clock, the hour hand is at 3 and the minute hand is at 12.
From the figure, we can see that there is a gap of 3 hour marks between the hour hand and the minute hand.
Therefore, angle between the hour hand and the minute hand at 3 o’clock = 3 x 30° = 90°
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Lines and Angles Class 6 Fill in the Blanks
Question 1.
A line has no endpoints and extends infinitely in ___________ directions.
Solution: both
We know that a line is a geometrical figure that is straight, has no width, and extends indefinitely in both directions.
Therefore, a line has no endpoints and extends infinitely in both directions.
Question 2.
If A and B are two points, the line segment between them is written as ____ .
Solution: \(\overline{A B}\) or \(\overline{B A}\)
We know that if A and B are two points, the line segment between them is written as \(\overline{A B}\) or \(\overline{B A}\).
Question 3.
The correct way to name an angle formed by points D, B and E in the given order, is ______ .
Solution: ∠DBE or ∠EBD
An angle is formed by two rays having a common starting point.
Given, the points are D, B and E.
So, the arms of the angle will be \(\overrightarrow{B D} \text { and } \overrightarrow{B E}\).
Thus, The correct way to name an angle formed by points D, B and E in the give order, is ∠DBE or ∠EBD.
Question 4.
The common starting point of the arms of an angle is called the ____ .
Solution: vertex
We know that the common starting point of the arms of an angle is called the vertex.
Question 5.
Any point outside the arms of an angle lies in its ______ .
Solution: exterior
We know that any point outside the arms of an angle lies in its exterior.
Question 6.
While comparing two angles using superimposition, their ____ and _____ must coincide.
Solution: vertices, one arm
While comparing two angles using superimposition, their vertices and one arm must coincide,
Question 7.
There are 360° in a _____ turn.
Solution: full
We know that there are 360° in a full turn.
Question 8.
When we fold a quarter circle in half again, the resulting angle is __________ .
Solution: 45°
We know that a full circle is 360°.
A quarter circle is 90°. If we fold that quarter circle i. e. 90° in half again, we get \(\frac{90^{\circ}}{2}\) = 45°.
So, when we fold a quarter circle in half again, the resulting angle is 45°.
Question 9.
Two times of 45° is a _____ angle.
Solution: right
Two times of 45° = 2 × 45° = 90°, which is a right angle.
Thus, two times of 45° is a right angle.
Question 10.
A line that divides an angle into two equal parts, is called _________ .
Solution: angle bisector
A line that divides an angle into two equal parts, is called angle bisector.