The document RD Sharma Solutions -Ex-11.2, Angles, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.

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**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 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?**

**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 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?**

**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 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?**

**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., 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.**

**Sol.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}**

**Sol.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.**

**Sol.11 :**

Right angle âˆ LMN

Obtuse angle âˆ 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 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.13 State the kind of each of the following angles :**

**Sol.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 :**

**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 0 ^{0} 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 0^{0} is called a zero angle.

**Q.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**

**Sol.4 : **(b) a right angle.

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

**Q.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**

**Sol.5 : **(c) a straight angle.

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

**Q.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**

**Sol.6 : **(d) a complete angle.

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

**Q.7. An angle of measure 240 ^{0} 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 240^{0} is called a reflex angle.

**Q.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.**

**Sol.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}.

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

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

**Sol.9 : **(b) 180^{0}

Since, 1 right angle = 90^{0}

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

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

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

**Sol.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}

**Q.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}**

**Sol.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}.