Exercise 11.1
Question 1: Give three examples of angles from your environment.
Solution 1: Below are the examples of angles:-
(1) Angles formed by the branch of a tree.
(2) Angle formed by the hour and minutes hands of clock.
(3) Angles formed by the walls of a room.
Question 2: Write the arms and the vertex of ∠LMP given in Fig. 11.14.
Solution 2:
Arms are = ML and MP.
Vertex of ∠LMP = M
Question 3: How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.
Solution 3:
Question 4: In Fig. 11.16, list the points which are: (i) in the interior of ∠ P (ii) in the exterior of ∠ P and (iii) lie on ∠ P.
Solution 4:
(i) Points J and C are the interior points of ∠P.
(ii) Points B and D are the exterior of ∠P.
(iii) Point M is lie on ∠P.
Question 5: In Fig. 11.17, write another name for:
(i) ∠ 1
(ii) ∠ 2
(iii) ∠ 3
(iv) ∠ 4
Solution 5:
(i) Another name of ∠ 1 is ∠ DOB or ∠ BOD.
(ii) Another name of ∠ 2 is ∠ BOC or ∠ COB.
(iii) Another name of ∠ 3 is ∠ COA or ∠ AOC.
(iv) Another name of ∠ 4 is ∠ AOD or ∠ DOA.
Question 6: In Fig. 11.18, write another name for:
(i) ∠ 1
(ii) ∠ 2
(iii) ∠ 3
Solution 6:
(i) Another name for ∠ 1 is ∠ EPB or ∠ BPE.
(ii) Another name for ∠ 2 is ∠ CQP or ∠ PQC.
(iii) Another name for ∠ 3 is ∠ DQF or ∠ FQD.
Question 7: In Fig. 11.19, which of the following statements are true:
Solution 1:
Below are the examples of right angle:
1.) Adjacent walls of a room are the example of right angle.
2.) Adjacent edges of a book are the example of right angle.
Below are the examples of acute angle:
1.) Adjacent sides of the letter Z are the example of acute angle.
2.) Adjacent fingers of our hand are the example of acute angle.
Below are the examples of obtuse angle:
1.) Two sloping sides of a roof are the example of obtuse angle.
2.) Two adjacent blades of a fan are the example of obtuse angle.
Question 2: An angle is formed by two adjacent fingers. What kind of angle will it appear?
Solution 2: Acute Angle will appear by two adjacent fingers.
Question 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 3:
(i) She will be rowing in the South-West direction. If she turns through a straight angle 180o.
(ii) She will be rowing in North-East direction. If she turns through a complete angle 360o.
Question 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 4:
(i) 90o North and West.
(ii) 180o North and South.
(iii) 135o North and South-East.
Question 5: A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it turn?
Solution 5: The angle is turns 90o from east to north direction.
Question 6: You are standing in a class-room facing north. In what direction are you facing after making a quarter turn?
Solution 6: If I making a quarter turn 90o i will facing towards east.
Question 7: A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Solution 7: The wheel of a bicycle is in the shape of circle so it is covers 360o in one turn.
(360°)/(90°) = 4 Right angles
A bicycle wheel makes 4 Right angles in a turn.
In four and half turns the bicycle wheel turns 4 × 4.5 = 18 Right angles
(i) 118o
(ii) 29o
(iii) 145o
(iv) 165o
(v) 0o
(vi) 75o
(vii) 180o
(viii) 89.5o
(ix) 30o
(x) 90o
(xi) 179o
(xii) 360o
(xiii) 90½o
Solution 10:
Question 11: Using only a ruler, draw an acute angle, a right angle and an obtuse angle in your notebook and name them.
Solution 11:
Solution 13:
Objective Type Questions ::->
Mark the correct alternative in each of the following:
Question 1: The vertex of an angles lies
(a) in its interior
(b) in its exterior
(c) on the angle
(d) inside the angle
Solution 1: (c)
The vertex of an angles lie on the angle.
Question 2: The figure formed by two rays with the same initial point is known as
(a) a ray
(b) a line
(c) an angle
(d) a line segment
Solution 2: (c)
The figure formed by two rays with the same initial point is known as an angle.
Question 3: An angle of measure 0° is called
(a) a complete angle
(b) a right angle
(c) a straight angle
(d) None of these
Solution 3: (d)
0° is called a zero angle.
Question 4: An angle of measure 90° is called
(a) a complete angle
(b) a right angle
(c) a straight angle
(d) a reflex angle
Solution 4: (b)
90° is called a right angle.
Question 5: An angle of measure 180° is called
(a) a zero angle
(b) a right angle
(c) a straight angle
(d) a reflex angle
Solution 5: (c)
180° is called a straight angle.
Question 6: An angle of measure 360° is called
(a) a zero angle
(b) a straight angle
(c) a reflex angle
(d) a complete angle
Solution 6: (d)
360° is called a complete angle.
Question 7: An angle of measure 240° is
(a) an acute angle
(b) an obtuse angle
(c) a straight angle
(d) a complete angle
Solution 7: There is no correct answer.
240° is called a reflex angle.
Question 8: A reflex angle measures
(a) more than 90° but less than 180°
(b) more than 180° but less than 270°
(c) more than 180° but less than 360°
(d) None of these
Solution 8: (c)
A reflex angle measures is more than 180° but less than 360°.
Question 9: The number of degrees in 2 right angles is
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Solution 9: (b)
2 right angles are 180°.
Question 10: The number of degrees in 3/2 right angles is
(a) 180°
(b) 360°
(c) 270°
(d) 90°
Solution 10: There is no correct answer.
Right angle = 90°
Right angle = 90°
3/2 × 90° = 135°
Question 11: If a bicycle wheel has 36 spokes, then the angle between a pair of adjacent spokes is
(a) 10°
(b) 15°
(c) 20°
(d) 12°
Solution 11: (a)
The wheel of a bicycle is in the shape of circle so central angle in a bicycle is 360o which consists of 36 spokes.
Thus, the angle between a pair of adjacent spokes is 10o