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
.