RD Sharma Solutions: Angles (Exercise 11.2)

# Angles (Exercise 11.2) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

``` Page 1

Exercise 11.2                                                                          page: 11.10
1. Give two examples each of right, acute and obtuse angles from your environment.
Solution:

The two examples of right angle are:
Two adjacent walls of a room and adjacent edges of a book

The two examples of acute angle are:
Two adjacent sides of the letter Z and two adjacent fingers of our hand.

The two examples of obtuse angles are:
Two sloping sides of a roof and two adjacent blades of a fan.

2. An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution:

The angle formed by two adjacent fingers will appear as acute angle.

3. Shikha is rowing a boat due north-east. In which direction will she be rowing if she turns it through:
(i) a straight angle
(ii) a complete angle.
Solution:

(i) If she turns through a straight angle (180
o
) she will be rowing in the South-West direction.

(ii) If she turns through a complete angle (360
o
) she will be rowing in North-East direction.

Page 2

Exercise 11.2                                                                          page: 11.10
1. Give two examples each of right, acute and obtuse angles from your environment.
Solution:

The two examples of right angle are:
Two adjacent walls of a room and adjacent edges of a book

The two examples of acute angle are:
Two adjacent sides of the letter Z and two adjacent fingers of our hand.

The two examples of obtuse angles are:
Two sloping sides of a roof and two adjacent blades of a fan.

2. An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution:

The angle formed by two adjacent fingers will appear as acute angle.

3. Shikha is rowing a boat due north-east. In which direction will she be rowing if she turns it through:
(i) a straight angle
(ii) a complete angle.
Solution:

(i) If she turns through a straight angle (180
o
) she will be rowing in the South-West direction.

(ii) If she turns through a complete angle (360
o
) she will be rowing in North-East direction.

4. What is the measure of the angle in degrees between:
(i) North and West?
(ii) North and South?
(iii) North and South- East?
Solution:

The measure of the angle in degrees between:
(i) North and West is 90
o
.

(ii) North and South is 180
o
.

(iii) North and South-East is 135
o
.

5. A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it
turn?
Solution:

It the ship moves from east to north direction, the angle it turns is 90
o
.

6. You are standing in a class-room facing north. In what direction are you facing after making a quarter
turn?
Solution:
By making a quarter turn (90
o
), I will be facing towards east if I turn to my right hand and if I turn to my left
hand, I will be facing towards west.

7. A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Solution:

We know that the wheel of a bicycle covers 360
o
in one turn.
It can be written as
Page 3

Exercise 11.2                                                                          page: 11.10
1. Give two examples each of right, acute and obtuse angles from your environment.
Solution:

The two examples of right angle are:
Two adjacent walls of a room and adjacent edges of a book

The two examples of acute angle are:
Two adjacent sides of the letter Z and two adjacent fingers of our hand.

The two examples of obtuse angles are:
Two sloping sides of a roof and two adjacent blades of a fan.

2. An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution:

The angle formed by two adjacent fingers will appear as acute angle.

3. Shikha is rowing a boat due north-east. In which direction will she be rowing if she turns it through:
(i) a straight angle
(ii) a complete angle.
Solution:

(i) If she turns through a straight angle (180
o
) she will be rowing in the South-West direction.

(ii) If she turns through a complete angle (360
o
) she will be rowing in North-East direction.

4. What is the measure of the angle in degrees between:
(i) North and West?
(ii) North and South?
(iii) North and South- East?
Solution:

The measure of the angle in degrees between:
(i) North and West is 90
o
.

(ii) North and South is 180
o
.

(iii) North and South-East is 135
o
.

5. A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it
turn?
Solution:

It the ship moves from east to north direction, the angle it turns is 90
o
.

6. You are standing in a class-room facing north. In what direction are you facing after making a quarter
turn?
Solution:
By making a quarter turn (90
o
), I will be facing towards east if I turn to my right hand and if I turn to my left
hand, I will be facing towards west.

7. A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Solution:

We know that the wheel of a bicycle covers 360
o
in one turn.
It can be written as

360/90 = 4 right angles
We know that in four and half turns the wheel turns by 4 (4.5) = 18 right angles

Hence, the number of right angles through which it turns is 18.

8. Look at your watch face. Through how many right angles does the minute-hand moves between 8: 00 O’
clock and 10: 30 O’ clock?
Solution:

We know that the time interval between 8: 00 O’ clock and 10: 30 O’ clock is two and half hours
The minute hand turns 360
o
in 1 hour
360/90 = 4 right angles
So in two and half hours the minute hand turns by 2.5 (4) = 10 right angles.

Hence, the minute hand turns by 10 right angles.

9. If a bicycle wheel has 48 spokes, then find the angle between a pair of adjacent spokes.
Solution:

The central angle in a bicycle is 360
o
which consists of 48 spokes.
So the angle between a pair of adjacent spokes = 360/48 = 7.5
o

Hence, the angle between a pair of adjacent spokes is 7.5
o
.

10. Classify the following angles as acute, obtuse, straight, right, zero and complete angle:
(i) 118
o

(ii) 29
o

(iii) 145
o

(iv) 165
o

(v) 0
o

(vi) 75
o

(vii) 180
o

(viii) 89.5
o

(ix) 30
o

(x) 90
o

(xi) 179
o

(xii) 360
o

(xiii) 90 ½
o

Solution:

(i) 118
o
is an obtuse angle.

(ii) 29
o
is an acute angle.

(iii) 145
o
is an obtuse angle.

(iv) 165
o
is an obtuse angle.

(v) 0
o
is a zero angle.

Page 4

Exercise 11.2                                                                          page: 11.10
1. Give two examples each of right, acute and obtuse angles from your environment.
Solution:

The two examples of right angle are:
Two adjacent walls of a room and adjacent edges of a book

The two examples of acute angle are:
Two adjacent sides of the letter Z and two adjacent fingers of our hand.

The two examples of obtuse angles are:
Two sloping sides of a roof and two adjacent blades of a fan.

2. An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution:

The angle formed by two adjacent fingers will appear as acute angle.

3. Shikha is rowing a boat due north-east. In which direction will she be rowing if she turns it through:
(i) a straight angle
(ii) a complete angle.
Solution:

(i) If she turns through a straight angle (180
o
) she will be rowing in the South-West direction.

(ii) If she turns through a complete angle (360
o
) she will be rowing in North-East direction.

4. What is the measure of the angle in degrees between:
(i) North and West?
(ii) North and South?
(iii) North and South- East?
Solution:

The measure of the angle in degrees between:
(i) North and West is 90
o
.

(ii) North and South is 180
o
.

(iii) North and South-East is 135
o
.

5. A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it
turn?
Solution:

It the ship moves from east to north direction, the angle it turns is 90
o
.

6. You are standing in a class-room facing north. In what direction are you facing after making a quarter
turn?
Solution:
By making a quarter turn (90
o
), I will be facing towards east if I turn to my right hand and if I turn to my left
hand, I will be facing towards west.

7. A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Solution:

We know that the wheel of a bicycle covers 360
o
in one turn.
It can be written as

360/90 = 4 right angles
We know that in four and half turns the wheel turns by 4 (4.5) = 18 right angles

Hence, the number of right angles through which it turns is 18.

8. Look at your watch face. Through how many right angles does the minute-hand moves between 8: 00 O’
clock and 10: 30 O’ clock?
Solution:

We know that the time interval between 8: 00 O’ clock and 10: 30 O’ clock is two and half hours
The minute hand turns 360
o
in 1 hour
360/90 = 4 right angles
So in two and half hours the minute hand turns by 2.5 (4) = 10 right angles.

Hence, the minute hand turns by 10 right angles.

9. If a bicycle wheel has 48 spokes, then find the angle between a pair of adjacent spokes.
Solution:

The central angle in a bicycle is 360
o
which consists of 48 spokes.
So the angle between a pair of adjacent spokes = 360/48 = 7.5
o

Hence, the angle between a pair of adjacent spokes is 7.5
o
.

10. Classify the following angles as acute, obtuse, straight, right, zero and complete angle:
(i) 118
o

(ii) 29
o

(iii) 145
o

(iv) 165
o

(v) 0
o

(vi) 75
o

(vii) 180
o

(viii) 89.5
o

(ix) 30
o

(x) 90
o

(xi) 179
o

(xii) 360
o

(xiii) 90 ½
o

Solution:

(i) 118
o
is an obtuse angle.

(ii) 29
o
is an acute angle.

(iii) 145
o
is an obtuse angle.

(iv) 165
o
is an obtuse angle.

(v) 0
o
is a zero angle.

(vi) 75
o
is an acute angle.

(vii) 180
o
is a straight angle.

(viii) 89.5
o
is an acute angle.

(ix) 30
o
is an acute angle.

(x) 90
o
is a right angle.

(xi) 179
o
is an obtuse angle.

(xii) 360
o
is a complete angle.

(xiii) 90 ½
o
is an obtuse angle.

11. Using only a ruler, draw an acute angle, a right angle and an obtuse angle in your notebook and name
them.
Solution:

12. State the kind of angle, in each case, formed between the following directions:
(i) East and West
(ii) East and North
(iii) North and North-East
(iv) North and South-East
Solution:

(i) East and West directions form a straight angle (180
o
).

(ii) East and North directions form a right angle (90
o
).

(iii) North and North-East directions form an acute angle (45
o
).

(iv) North and South-East directions form an obtuse angle (135
o
).

13. State the kind of each of the following angles:
Page 5

Exercise 11.2                                                                          page: 11.10
1. Give two examples each of right, acute and obtuse angles from your environment.
Solution:

The two examples of right angle are:
Two adjacent walls of a room and adjacent edges of a book

The two examples of acute angle are:
Two adjacent sides of the letter Z and two adjacent fingers of our hand.

The two examples of obtuse angles are:
Two sloping sides of a roof and two adjacent blades of a fan.

2. An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution:

The angle formed by two adjacent fingers will appear as acute angle.

3. Shikha is rowing a boat due north-east. In which direction will she be rowing if she turns it through:
(i) a straight angle
(ii) a complete angle.
Solution:

(i) If she turns through a straight angle (180
o
) she will be rowing in the South-West direction.

(ii) If she turns through a complete angle (360
o
) she will be rowing in North-East direction.

4. What is the measure of the angle in degrees between:
(i) North and West?
(ii) North and South?
(iii) North and South- East?
Solution:

The measure of the angle in degrees between:
(i) North and West is 90
o
.

(ii) North and South is 180
o
.

(iii) North and South-East is 135
o
.

5. A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it
turn?
Solution:

It the ship moves from east to north direction, the angle it turns is 90
o
.

6. You are standing in a class-room facing north. In what direction are you facing after making a quarter
turn?
Solution:
By making a quarter turn (90
o
), I will be facing towards east if I turn to my right hand and if I turn to my left
hand, I will be facing towards west.

7. A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Solution:

We know that the wheel of a bicycle covers 360
o
in one turn.
It can be written as

360/90 = 4 right angles
We know that in four and half turns the wheel turns by 4 (4.5) = 18 right angles

Hence, the number of right angles through which it turns is 18.

8. Look at your watch face. Through how many right angles does the minute-hand moves between 8: 00 O’
clock and 10: 30 O’ clock?
Solution:

We know that the time interval between 8: 00 O’ clock and 10: 30 O’ clock is two and half hours
The minute hand turns 360
o
in 1 hour
360/90 = 4 right angles
So in two and half hours the minute hand turns by 2.5 (4) = 10 right angles.

Hence, the minute hand turns by 10 right angles.

9. If a bicycle wheel has 48 spokes, then find the angle between a pair of adjacent spokes.
Solution:

The central angle in a bicycle is 360
o
which consists of 48 spokes.
So the angle between a pair of adjacent spokes = 360/48 = 7.5
o

Hence, the angle between a pair of adjacent spokes is 7.5
o
.

10. Classify the following angles as acute, obtuse, straight, right, zero and complete angle:
(i) 118
o

(ii) 29
o

(iii) 145
o

(iv) 165
o

(v) 0
o

(vi) 75
o

(vii) 180
o

(viii) 89.5
o

(ix) 30
o

(x) 90
o

(xi) 179
o

(xii) 360
o

(xiii) 90 ½
o

Solution:

(i) 118
o
is an obtuse angle.

(ii) 29
o
is an acute angle.

(iii) 145
o
is an obtuse angle.

(iv) 165
o
is an obtuse angle.

(v) 0
o
is a zero angle.

(vi) 75
o
is an acute angle.

(vii) 180
o
is a straight angle.

(viii) 89.5
o
is an acute angle.

(ix) 30
o
is an acute angle.

(x) 90
o
is a right angle.

(xi) 179
o
is an obtuse angle.

(xii) 360
o
is a complete angle.

(xiii) 90 ½
o
is an obtuse angle.

11. Using only a ruler, draw an acute angle, a right angle and an obtuse angle in your notebook and name
them.
Solution:

12. State the kind of angle, in each case, formed between the following directions:
(i) East and West
(ii) East and North
(iii) North and North-East
(iv) North and South-East
Solution:

(i) East and West directions form a straight angle (180
o
).

(ii) East and North directions form a right angle (90
o
).

(iii) North and North-East directions form an acute angle (45
o
).

(iv) North and South-East directions form an obtuse angle (135
o
).

13. State the kind of each of the following angles:

Solution:

(i) Acute angle which measures between 0
o
and 90
o
.

(ii) Obtuse angle which measures between 90
o
and 180
o
.

(iii) Straight angle which measures 180
o
.

(iv) Right angle which measures 90
o
.

(v) Complete angle which measures 360
o
.

```

## Mathematics (Maths) Class 6

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## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

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