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
.
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