## RD Sharma Solutions Class 6 Chapter 11 Exercise 11.2

Exercise 11.2

Q.1) Give two examples each of right, acute and obtuse angles from your environment.

Soln.1 :

Two examples of right angle in our environment are:

(i) The angle formed by the two adjacent walls of a room is a right angle.

(ii) The angle formed by the two adjacent edges of a book is a right angle.

Two examples of acute angle in our environment are:

(i) The angle formed between the two adjacent fingers of our hand.

(ii) The angle between the two adjacent sides of the letter Z of English alphabet.

Two examples of obtuse angle in our environment are:

(i) The smaller angle formed by the two adjacent blades of a fan.

(ii) The smaller angle formed by the two sloping sides of a roof of a but is an obtuse angle.

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

Soln.2 :

Angle formed by two adjacent fingers will appear as an acute angle.

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

Soln.3 :

(i) If Shikha turns through a straight angle or 180 degrees, she will be rowing along the south â€“ west direction.

(ii) If Shikha turns through a complete angle or 360 degrees, she will be rowing along her original direction, i.e., north â€“ east direction.

Q.4 What is the measure of the angle in degrees between :

(i) North and West?

(ii) North and South?

(iii) North and South â€“ East?

Soln.4 :

The measure of the angle between :

(i) North and West is 90 degrees.

(ii) North and South is 180 degrees.

(iii) North and South â€“ East is 135 degrees.

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

Soln.5 :

If the ship is sailing in east direction and turns to north direction, it turns through an angle of 90 degrees.

Q.6 You are standing in a class room facing north. In what direction are you facing after making a quarter turn?

Soln.6 :

After making a quarter turn or a turn of 90 degrees, i will be facing east if i turn to my right hand. Similarly, if i turn to my left hand, i will be facing west.

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

Soln.7 :

In one turn, the wheel of a bicycle covers 360Â°.

If we express 360Â° in right angles, we get :

360Â°/90Â° = 4 right angles.

Thus, in four and a half turns, the wheel will turn by (4 x 4.5) = 18 right angles.

Q.8 Look at your watch face. Through how many right angles does the minute hand moves between 8 Oâ€™ clock and 10:30 Oâ€™ clock?

Soln.8 :

The time interval between 8 : 00 O’clock and 10 : 30 O’clock is 2.5 hours, i.e., two and a half hours.

In 1 hour, the minute hand turns by a complete angle, i.e., 360Â° or 360Â°/90Â° = 4 right angles.

Thus, in 2.5 hours, the minute hand will turn by 2.5 x 4 = 10 right angles.

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

Soln.9 :

In a bicycle, the central angle measures 360^{0} and it consists of 48 spokes.

Therefore, angle between any two adjacent spokes = 360/48 = 7.5^{0}.

Q.10 Classify the following angles as acute, obtuse, straight, right, zero and complete angle:

(i) 118^{0}

(ii) 29^{0}

(iii) 145^{0}

(iv) 165^{0}

(v) 0^{0}

(vi) 75^{0}

(vii) 180^{0}

(viii) 89.5^{0}

(ix) 30^{0}

(x) 90^{0}

(xi) 179^{0}

(xii) 360^{0}

(xiii) 90.5^{0}

Soln.10 :

An acute angle measures between 0Â° and 90Â° ; an obtuse angle measures between 90Â° and 180Â° ; a straight angle measures 180Â° ; a right angle measures 90Â° ; a zero angle measures 0Â° and a complete angle measures 360Â°.

(i) 118Â° is an obtuse angle.

(ii) 29Â° is an acute angle.

(iii) 145Â° is an obtuse angle.

(iv) 165Â° is an obtuse angle.

(v) 0Â° is a zero angle.

(vi) 75Â° is an acute angle.

(vii) 180Â° is a straight angle.

(viii) 89.5Â° is an acute angle.

(ix) 30Â° is an acute angle.

(x) 90Â° is a right angle.

(xi) 179Â° is an obtuse angle.

(xii) 360Â° is a complete angle.

(xiii) 90.5Â° is an obtuse angle.

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

Soln.11 :

Right angle \( \angle LMN \)

Obtuse angle \( \angle PQR \)

Q.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

Soln.12:

(i) East and west directions form an angle of 180Â°, which is a straight angle.

(ii) East and north directions form an angle of 90Â°, which is a right angle.

(iii) North and north-east directions form an angle of 45Â°, which is an acute angle.

(iv) North and south-east directions form an angle of 135Â°, which is an obtuse angle.

Q.14 State the kind of each of the following angles :

Soln.13 :

(i) Acute angle, as it measures between 0Â° and 90Â°.

(ii) Obtuse angle, as it measures between 90Â° and 180Â°.

(iii) Straight angle, as it is equal to 180Â°.

(iv) Right angle, as it is equal to 90Â°.

(v) Complete angle, as it is equal to 360Â°.

OBJECTIVE TYPE QUESTIONS :

Mark the correct alternative in each of the following :

1. The vertex of an angle lies

(a) in its interior (b) in its exterior (c) on the angle (d) inside the angle

Soln.1 :

(c) on the angle.

The vertex of an angle lies on the angle.

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

Soln.2 :

(c) an angle.

An angle is a figure by two rays with the same initial point.

3. An angle of measure 0^{0} is called

(a) a complete angle (b) a right angle (c) a straight angle (d) none of these

Soln.3 :

(d) none of these.

An angle of measure 0^{0} is called a zero angle.

4. An angle of measure 90^{0} is called

(a) a complete angle (b) a right angle (c) a straight angle (d) a reflex angle

Soln.4 :

(b) a right angle.

An angle of measure 90^{0} is called a right angle.

5. An angle of measure 180^{0} is called

(a) a zero angle (b) a right angle (c) a straight angle (d) a reflex angle

Soln.5 :

(c) a straight angle.

An angle of measure 180^{0} is a straight angle.

6. An angle of measure 360^{0} is called

(a) a zero angle (b) an straight angle (c) a reflex angle (d) a complete angle

Soln.6 :

(d) a complete angle.

An angle of measure 360^{0} is called a complete angle.

7. An angle of measure 240^{0} is

(a) an acute angle (b) an obtuse angle (c) a straight angle (d) a complete angle

Soln.7 :

None of the given options are correct.

An angle of measure 240^{0} is called a reflex angle.

8. A reflex angle measures

(a) more than 90^{0} but less than 180^{0} (b) more than 180^{0} but less than 270^{0} (c) more than 180^{0} but less than 360^{0 } (d) none of these.

Soln.8 :

(c) more than 180^{0} but less than 360^{0}

A reflex angle is defined as an angle that measures more than 180^{0} but less than 360^{0}.

9. The number of degrees in 2 right angles is

(a) 90^{0 } (b) 180^{0} (c) 270^{0} (d) 360^{0}

Soln.9 :

(b) 180^{0}

Since, 1 right angle = 90^{0}

Therefore, 2 right angles = 90^{0} x 2 = 180^{0}

10. The number of degrees in 3/2 right angles is

(a) 180^{0 } (b) 360^{0 } (c) 270^{0} (d) 90^{0}

Soln.10 :

None of the options are correct.

The correct answer is 135^{0}

Since, 1 right angle = 90^{0}

Therefore, 3/2 right angles = 3/2 x 90^{0 }= 135^{0}

11. If bicycle wheel has 36 spokes, then the angle between a pair of adjacent spokes is

(a) 10^{0} (b) 15^{0} (c) 20^{0} (d) 12^{0}

Soln.11 :

(a) 10^{0}

The complete angle of bicycle wheel measures is 360^{0}.

Therefore, the angle between two adjacent spokes of the containing 36 spokes = 360/36 = 10^{0}.