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 .Read More

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