Lines and Angles Class 6 Worksheet with Answers Maths Chapter 2

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Class 6 Maths Chapter 2 Lines and Angles Worksheet with Answers Pdf

Lines and Angles Class 6 Maths Worksheet

Class 6 Maths Chapter 2 Worksheet with Answers – Class 6 Lines and Angles Worksheet

Multiple choice questions.

1. A contains a countless number of points.
(a) point
(b) line segment
(c) ray
(d) line
Answer:
(d) line

2. Which figure represents : point P lies on line segment AB.

Answer:
(a)

3. How many points does the given figure has?

(a) 5
(b) 4
(c) 3
(d) 6
Answer:
(a) 5

4. A line segment has
(a) definite length but no end points
(b) infinite length but no end point
(c) definite length and have end points
(d) None of the above
Answer:
(c) definite length and have end points

5. How many lines pass through two given points?
(a) One
(b) Two
(c) Many
(d) None
Answer:
(a) One

6. If two lines are perpendicular to each other, then angle between them at the point of contact is
(a) 80°
(b) 90°
(c) 85°
(d) 100°
Answer:
(b) 90°

7. One of the acute angle of a right triangle is 75°. Find the other acute angle,
(a) 25°
(b) 15°
(c) 35°
(d) 45°
Answer:
(b) 15°

8. If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?
(a) One obtuse angle and one acute angle
(b) One reflex angle and one acute angle
(c) Two obtuse angles
(d) Two right angles CD
Answer:
(d) Two right angles CD

9. In the figure given below, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of ∠BPY is

(a) greater than 45°.
(b) equal to 45°.
(C) less than 45°
(d) 90°.
Answer:
(b) equal to 45°.

10. If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
(a) One obtuse angle and one acute angle
(b) One right angle and one acute angle
(c) Two acute angles
(d) Two right angles
Answer:
(d) Two right angles

11. Which of the following angles will form a straight angle?
(a) 90°, 90°
(b) 45°, 45°
(c) 45°, 60°
(d) 55°, 75°
Answer:
(a) 90°, 90°

12. What is the name of angle in the given figure?

(a) Right
(b) Acute
(c) Reflex
(d) Obtuse
Answer:
(c) Reflex

13. A line segment AB is denoted as
(a) \(\overline{A B}\)
(b) \(\overleftrightarrow{A B}\)
(c) AB
(d) Both (a) and (b)
Answer:
(a) \(\overline{A B}\)

(b) If the length of a line segment AB = 3 cm, then 2AB will be
(a) 8 cm
(b) 6 cm
(c) 4 cm
(d) 9 cm
Answer:
(b) 6 cm

14. In the figure given below, the number of obtuse angles is

(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(c) 4

15. To construct an angle of 67.5°, we need to bisect the angle of
(a) 135°
(b) 120°
(c) 150°
(d) 167.5°
Answer:
(a) 135°

16. What will be the angle at 3 o’clock?
(a) 90°
(b) 45°
(c) 30°
(d) 60°
Answer:
(a) 90°

17. One full rotation of angle is equal to
(a) 180°
(b) 360°
(c) 90°
(d) 270°
Answer:
(b) 360°

Assertion & Reason

Study the Assertion (A) and Reason (R) statements given below and choose the correct alternative.
(i) Assertion (A) A line contains a countless number of points.
Reason (R) Line extends indefinitely in both the directions.
(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.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.

(ii) Assertion (A) DE and DF are two rays having initial point D.

Reason (R) A ray is a portion of a line. It starts at one point (called starting point) and goes endlessly in a direction.
(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.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

(iii) Assertion (A) Line segments have two end points.
Reason (R) Line segments have indefinite length.
(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.
Answer:
(c) A is true but R is false.

(iv) Assertion (A) To construct an angle of 45°, we first draw a right angle and then bisect it using a ruler and pair of compasses.
Reason (R) 45° is multiple of 15°. So, it can be drawn using ruler and pair of compasses.
(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.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.

(v) Assertion (A) If angles a and b form a straight-line pair of angles and a = 40°, then
b = 150°.
Reason (R) Sum of straight line pair of angles is always 180°.
(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.
Answer:
(d) A is false but R is true.

(vi) Assertion (A) If the angle formed by meeting of two rays goes beyond a right angle, it is obtuse.
Reason (R) An obtuse angle has a measurement greater than 90° but less than

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

Fill in the blanks.

1. A geometrical figure which determines a location but has no length, breadth and thickness is called a __________.
Answer:
point

2. A __________ is obtained when a segment is extended on both sides indefinitely.
Answer:
Line

3. The shortest distance between two points with a fixed length is a __________.
Answer:
Line segment

4. From a given point, __________ rays can be drawn.
Answer:
Infinite

5. A __________ is a portion of a line starting at a point and extending in one direction indefinitely.
Answer:
Ray

6. __________ lines can be drawn from one point.
Answer:
Infinite

7. A line has __________ length.
Answer:
Indefinite

8. AB and BA denote the __________ rays.
Answer:
Different

9. An angle is made up of two _________ starting from a common point.
Answer:
Rays

10. The two rays forming the angle are called _________ of the angle.
Answer:
Arms

11. The common starting point of the angle is called the _________ of the angle.
Answer:
Vertex

12. Degree measures of angles can be measured using a _________.
Answer:
Protractor

13. An angle greater than 180° and less than a complete angle is called _________.
Answer:
Reflex

14. One full rotation angle is equivalent to _________ degrees.
Answer:
360°

15. The line that bisects a given angle is called the _________ of the angle.
Answer:
Angle bisector

16. Two lines that meet at right angles are called _________ lines.
Answer:
Perpendicular

State whether the following statements are True or False.

1. A line segment AB is symbolically written as AB.
Answer:
False

2. A point is a dimensionless geometrical figure.
Answer:
True

3. A line segment is determined by two points in a plane.
Answer:
True

4. A line has no end point.
Answer:
True

5. A ray OP is symbolically written as OP.
Answer:
True

6. A ray determines a precise location.
Answer:
False

7. Two angles can have exactly five points in common.
Answer:
False

8. Reflex angles are greater than straight angles.
Answer:
True

9. If two adjacent angles are equal, then each angle is 90°.
Answer:
False

10. If two angles form a straight line, both can be acute angles.
Answer:
False

11. If m∠A = 73° and m∠B = 37°, then m∠A > m∠B.
Answer:
True

Match the following

Question 1.
Match the following properties with their correct geometrical figures.

Column A	Column B
(i) Indefinite length in both the directions	(a) Ray
(ii) Has no size but shows position	(b) Line
(hi) Countless collection of points which is a part of line with two end points	(c) Point
(iv) Indefinite length in one direction	(d) Line segment

Answer:

Column A	Column B
(i) Indefinite length in both the directions	(b) Line
(ii) Has no size but shows position	(c) Point
(hi) Countless collection of points which is a part of line with two end points	(d) Line segment
(iv) Indefinite length in one direction	(a) Ray

Question 2.
Match the following

Column A	Column B
(i) Straight angle	(a) Less than one-fourth of a revolution
(ii) Right angle	(b) More than half a revolution
(iii) Acute angle	(c) Half of a revolution
(iv) Obtuse angle	(d) One-fourth of a revolution
(v) Reflex angle	(e) Between \(\frac{1}{4}\) and \(\frac{1}{2}\) of a revolution

Answer:

Column A	Column B
(i) Straight angle	(c) Half of a revolution
(ii) Right angle	(d) One-fourth of a revolution
(iii) Acute angle	(a) Less than one-fourth of a revolution
(iv) Obtuse angle	(e) Between \(\frac{1}{4}\) and \(\frac{1}{2}\) of a revolution
(v) Reflex angle	(b) More than half a revolution

Complete the following table.

Question 1.

Answer:
(i) \(\overline{A B}\)
(ii) \(\overrightarrow{A B}, \overrightarrow{A C}, \overrightarrow{A E}\)
(iii) \(\overline{A B}, \overline{B C}, \overline{C D}\)
(iv) \(\overline{B A}\)

Question 2.
Complete the following table by naming the angles in the given figure.

(i) ∠1 = ∠CBD
(ii) ∠2 ____________
(hi) ∠1 + ∠2 ____________
(iv) ∠2 + ∠3 ____________
(y) ∠1 + ∠2 + ∠3 ____________
(vi) ∠CBA – ∠1 ____________
Answer:
(ii) ∠DBE
(iii) ∠CBE
(iv) ∠DBA
(v) ∠CBA
(vi) ∠DBA

Case-based questions.

Question 1.
A math’s teacher was teaching students about intersecting lines. Suppose AB and CD are two lines, which meets at point 0. In this point 0, she draws a line OE and all these lines were making different angles with each other.

After explaining the description of the figure, she asked the following questions from the students.
On the basis of the above information, solve the following questions.
(i) Find the measure of ∠BOD.
___________________________________________
Answer:
∠BOD = 35°

(ii) Check whether pair of angles ∠AOC and ∠BOC makes a straight angle pair.
___________________________________________
Answer:
From figure, it is clear that
∠AOC + ∠BOC = 180°, because AB is a straight line.
Hence, ∠AOC and ∠BOC make a straight angle pair.

(iii) Which of the following angles do not form straight angles?
(a) ∠AOB
(b) ∠COE
Answer:
(b) ∠COE

(iv) Find the measure of ∠AOE.
___________________________________________
Answer:
70°

Question 2.
A student observe a clock. The hour hand and minute hand create various angles throughout the day.

Answer the following questions
(i) What type of angle is formed between the hour and minute hands at 6:00?
(a) Actue
(b) Obtuse
(c) Straight
(d) Reflex
Answer:
(c) Straight

(ii) If the hour hand points at 2 and the minute hand points at 7, what is the measure of angle formed?
(a) 120°
(b) 150°
(c) 100°
(d) 180°
Answer:
(b) 150°

(iii) What will be measure of angle at 4:00?
(a) 120°
(b) 100°
(c) 90°
(d) 150°
Answer:
(a) 120°

Very Short Answer Type Questions.

Question 1.
Draw a rough figure and label suitably when line l contains E and F, but not D.
___________________________________________
Answer:

Question 2.
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the given figure.

___________________________________________
Answer:
\(\overleftrightarrow{A B}, \overleftrightarrow{A C}, \overleftrightarrow{A D}, \overleftrightarrow{C D}, \overleftrightarrow{B C}, \overleftrightarrow{D A}, \overleftrightarrow{D B}, \overleftrightarrow{D C}, \overleftrightarrow{B D}, \overleftrightarrow{C A}, \overleftrightarrow{C B},\overleftrightarrow{B A}\)

Question 3.
Use the given figure to name the following.

(a) Five points ___________________________________________
(b) Aline ___________________________________________
(c) Four rays ___________________________________________
(d) Five line segments ___________________________________________
Answer:
(a) B, C, D, E and A
(b) DB (or BD)
(c) OB, OC, OD, 04
(d) OB, OC, OD, OE and DE

Short Answer Type Questions

Question 1.
Refer to the figure given below and answer the following.

(a) Number of angles less than 180° and their names.
___________________________________________
Answer:
12 : ∠OAB, ∠OBA, ∠OAC, ∠OCA, ∠OCD, ∠ODC, ∠AOB, ∠AOC, ∠COD, ∠DOB, ∠BAC, ∠ACD

(b) Number of straight-line angles.
___________________________________________
Answer:
Four

Question 2.
Write down fifteen angles (less than 180°) involved in the figure given below.

___________________________________________
___________________________________________
Answer:
∠EAD, ∠AEF, ∠EFD, ∠ADF, ∠DFC, ∠DCF, ∠CDF, ∠BEF, ∠BFE, ∠EFB, ∠FBC, ∠FCB, ∠BFC, ∠ABC, ∠ACB

Question 3.
Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate.
___________________________________________
___________________________________________
Answer:
Do it yourself

Question 4.
In the figure given below.

(a) Name any four angles that appear to be acute angles.
___________________________________________
Answer:
∠AEB, ∠ADE, ∠BAE, ∠BCE

(b) Name any two angles that appear to be obtuse angles.
___________________________________________
Answer:
∠BCD, ∠BAD

Long Answer Type Questions.

Question 1.
Can we have two acute angles whose sum is
(a) an acute angle? Why or why not? ____________
(b) a right angle? Why or why not? ____________
(c) an obtuse angle? Why or why not? ____________
(d) a straight angle? Why or why not? ____________
(e) a reflex angle? Why or why not? ____________
Answer:
(a) Yes, The sum of two acute angles may be less than a right angle.
(b) Yes, The sum of two acute angles may be equal to a right angle.
(c) Yes, The sum of two acute angles may be more than a right angle.
(d) No, The sum of two acute angles is always less than 180°.
(e) No, The sum of two acute angles is always less than 180°.

Question 2.
Write another name for the following angles in the given figure.

(a) ∠1 ____________
(b) ∠2 ____________
(c) ∠3 ____________
(d) ∠4 ____________
(e) ∠5 ____________
(f) ∠6 ____________
Answer:
(a) ∠BAC or ∠CAB
(b) ∠ABC or ∠CBA
(c) ∠BEF or ∠FEB
(d) ∠ADC or ∠CDA
(e) ∠CFG or ∠GFC
(f) ∠DGF or ∠FGD

Activity

Question 1.
Take a sheet of paper and draw diagrams of two angles such that they have
(a) one point in common.
(b) two points in common.
(c) three points in common.
(d) four points in common.
(e) one ray in common.
Answer:
Do it yourself

Question 2.
Draw a rough sketch of the diagram given below as per the dimensions of your choice and answer the questions that follow.

(a) What is AE + EC ?
(b) What is AC – EC?
(c) What is BD- BE?
(d) What is BD – DE?
Answer:
Do it yourself

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