Ex-11.2, Angles, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

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

Sol.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?

Sol.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.

Sol.3 : (i) If Shikha turns through a straight angle or 180 degrees, she will be rowing along the south – west direction.

(ii) If Shikha turns through a complete angle or 360 degrees, she will be rowing along her original direction, i.e., north – 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 – East?

Sol.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 – 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?

Sol.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?

Sol.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.

Sol.7 : In one turn, the wheel of a bicycle covers 360°.

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

360°/90° = 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 O’ clock and 10:30 O’ clock?

Sol.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., 360° or 360°/90° = 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.

Sol.9 : In a bicycle, the central angle measures 360⁰ and it consists of 48 spokes.

Therefore, angle between any two adjacent spokes = 360/48 = 7.5⁰.

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

(i) 118⁰

(ii) 29⁰

(iii) 145⁰

(iv) 165⁰

(v) 0⁰

(vi) 75⁰

(vii) 180⁰

(viii) 89.5⁰

(ix) 30⁰

(x) 90⁰

(xi) 179⁰

(xii) 360⁰

(xiii) 90.5⁰

Sol.10 : An acute angle measures between 0° and 90° ; an obtuse angle measures between 90° and 180° ; a straight angle measures 180° ; a right angle measures 90° ; a zero angle measures 0° and a complete angle measures 360°.

(i) 118° is an obtuse angle.

(ii) 29° is an acute angle.

(iii) 145° is an obtuse angle.

(iv) 165° is an obtuse angle.

(v) 0° is a zero angle.

(vi) 75° is an acute angle.

(vii) 180° is a straight angle.

(viii) 89.5° is an acute angle.

(ix) 30° is an acute angle.

(x) 90° is a right angle.

(xi) 179° is an obtuse angle.

(xii) 360° is a complete angle.

(xiii) 90.5° 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.

Sol.11 :

Right angle ∠LMN

Obtuse 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

Sol.12: (i) East and west directions form an angle of 180°, which is a straight angle.

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

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

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

Q.13 State the kind of each of the following angles :

Sol.13 :

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

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

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

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

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

OBJECTIVE TYPE QUESTIONS :

Mark the correct alternative in each of the following :

Q.1. The vertex of an angle lies

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

Sol.1 : (c) on the angle.

The vertex of an angle lies on the angle.

Q.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

Sol.2 : (c) an angle.

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

Q.3. An angle of measure 0⁰ is called

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

Sol.3 : (d) none of these.

An angle of measure 0⁰ is called a zero angle.

Q.4. An angle of measure 90⁰ is called

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

Sol.4 : (b) a right angle.

An angle of measure 90⁰ is called a right angle.

Q.5. An angle of measure 180⁰ is called

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

Sol.5 : (c) a straight angle.

An angle of measure 180⁰ is a straight angle.

Q.6. An angle of measure 360⁰ is called

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

Sol.6 : (d) a complete angle.

An angle of measure 360⁰ is called a complete angle.

Q.7. An angle of measure 240⁰ is

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

Sol.7 : None of the given options are correct.

An angle of measure 240⁰ is called a reflex angle.

Q.8. A reflex angle measures

(a) more than 90⁰ but less than 180⁰ (b) more than 180⁰ but less than 270⁰ (c) more than 180⁰ but less than 360⁰ (d) none of these.

Sol.8 : (c) more than 180⁰ but less than 360⁰

A reflex angle is defined as an angle that measures more than 180⁰ but less than 360⁰.

Q.9. The number of degrees in 2 right angles is

(a) 90⁰ (b) 180⁰ (c) 270⁰ (d) 360⁰

Sol.9 : (b) 180⁰

Since, 1 right angle = 90⁰

Therefore, 2 right angles = 90⁰ x 2 = 180⁰

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

(a) 180⁰ (b) 360⁰ (c) 270⁰ (d) 90⁰

Sol.10 : None of the options are correct.

The correct answer is 135⁰

Since, 1 right angle = 90⁰

Therefore, 3/2 right angles = 3/2 x 90⁰ = 135⁰

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

(a) 10⁰ (b) 15⁰ (c) 20⁰ (d) 12⁰

Sol.11 : (a) 10⁰

The complete angle of bicycle wheel measures is 360⁰.

Therefore, the angle between two adjacent spokes of the containing 36 spokes = 360/36 = 10⁰.