Rd Sharma 2018 Solutions for Class 6 Math Chapter 11 Angles are provided here with simple step-by-step explanations. These solutions for Angles are extremely popular among Class 6 students for Math Angles Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 6 Math Chapter 11 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 6 Math are prepared by experts and are 100% accurate.

#### Page No 11.10:

#### Question 1:

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

#### Answer:

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 hut is an obtuse angle.

#### Page No 11.10:

#### Question 2:

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

#### Answer:

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

#### Page No 11.10:

#### 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

#### Answer:

(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.

#### Page No 11.10:

#### 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?

#### Answer:

The measure of the angle between:

(i) North and west is 90^{o}.â€‹

(ii) North and South is 180^{o}.â€‹

(iii) North and South-East is 135^{o}.â€‹

#### Page No 11.10:

#### Question 5:

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

#### Answer:

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

#### Page No 11.10:

#### Question 6:

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

#### Answer:

After making a quarter turn or a turn of 90^{o},â€‹ 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.

#### Page No 11.10:

#### Question 7:

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

#### Answer:

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

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

$\frac{\mathrm{360\u02da}}{\mathrm{90\u02da}}$ = 4 right angles

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

#### Page No 11.10:

#### Question 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?

#### Answer:

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., 360Ëš or 360Ëš/90Ëš = 4 right angles.

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

#### Page No 11.10:

#### Question 9:

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

#### Answer:

In a bicycle, the central angle measures 360Ëš and it consists of 48 spokes.

$\therefore $ Angle between any two adjacent spokes = $\frac{360}{48}$ = 7.5Ëš

#### Page No 11.10:

#### Question 10:

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

(i) 118°

(ii) 29°

(iii) 145°

(iv) 165°

(v) 0°

(vi) 75°

(vii) 180°

(viii) 89.5°

(ix) 30°

(x) 90°

(xi) 179°

(xii) 360°

(xiii) $90{\frac{1}{2}}^{0}$

#### Answer:

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$\frac{1}{2}$° is an obtuse angle.

#### Page No 11.10:

#### Question 11:

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

#### Answer:

Acute angle ∠ABC Right angle ∠LMN Obtuse angle ∠PQR

#### Page No 11.10:

#### Question 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

#### Answer:

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

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

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

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

#### Page No 11.11:

#### Question 13:

State the kind of each of the following angles:

#### Answer:

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

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

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

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

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

#### Page No 11.11:

#### Question 1:

The vertex of an angles lies

(a) in its interior

(b) in its exterior

(c) on the angle

(d) inside the angle

#### Answer:

(c) on the angle

The vertex of an angle lies on the angle.

#### Page No 11.11:

#### 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

#### Answer:

(c) an angle

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

#### Page No 11.11:

#### 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

#### Answer:

(d) None of these

An angle of measure 0° is called a zero angle.

#### Page No 11.11:

#### 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

#### Answer:

(b) a right angle

An angle of measure 90° is called a right angle.

#### Page No 11.11:

#### 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

#### Answer:

(c) a straight angle

An angle of measure 180° is called a straight angle.

#### Page No 11.12:

#### 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

#### Answer:

(d) a complete angle

An angle of measure 360° is called a complete angle.

#### Page No 11.12:

#### Question 7:

An angle of measure 240° is

(a) an acute angle

(b) an obtuse angle

(c) a straight angle

(d) a complete angle

#### Answer:

None of the given options are correct.

An angle of measure 240° is called a reflex angle.

#### Page No 11.12:

#### 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

#### Answer:

(c) more than 180° but less than 360°

A reflex angle is defined as an angle that measures more than 180° but less than 360°.

#### Page No 11.12:

#### Question 9:

The number of degrees in 2 right angle is

(a) 90°

(b) 180°

(c) 270°

(d) 360°

#### Answer:

(b) 180°

$\because $ 1 right angle = 90°

$\therefore $ 2 right angles = 90°â€‹ × 2 = 180°

#### Page No 11.12:

#### Question 10:

The number of degrees in $\frac{3}{2}$ right angles is

(a) 180°

(b) 360°

(c) 270°

(d) 90°

#### Answer:

None of the options are correct.

The correct answer is 135°.

$\because $ 1 right angle = 90°

$\therefore $ $\frac{3}{2}$ right angles = $\frac{3}{2}$ × 90° = 135°

#### Page No 11.12:

#### 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°

#### Answer:

(a) 10°

The complete central angle of a bicycle wheel measures 360°.

Therefore, the angle between two adjacent spokes of the wheel containing 36 spokes = $\frac{360}{36}$ = 10°

#### Page No 11.5:

#### Question 1:

Give three examples of angles from your environment.

#### Answer:

Three examples of angles from our environment are:

(i) Angle formed by the minute and hour hands of an analog clock

(ii) Angle formed by the two adjacent walls of a room

(iii) Angle formed by the two adjacent fingers of our hand

#### Page No 11.5:

#### Question 2:

Write the arms and the vertex of ∠LMP given in Fig. 11.14.

#### Answer:

Arms of ∠LMP are MP and ML. Further, its vertex is M.

#### Page No 11.5:

#### Question 3:

How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

#### Answer:

(i) Three angles are formed, namely ∠ABC, ∠BAC and ∠ACB.

(ii) Four angles are formed, namely ∠ABC, ∠ADC, ∠BCD and ∠BAD.

(iii) Eight angles are formed namely, ∠ADC, ∠ACD, ∠DAC, ∠ACB, ∠ABC, ∠BAC, ∠BCD and ∠BAD.

#### Page No 11.6:

#### 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*.

#### Answer:

(i) Points J and C lie in the interior of ∠*P*.

(ii) Points D and B lie in the exterior of ∠*P*.

(iii) Points A, P and M lie on ∠*P**.*

#### Page No 11.6:

#### Question 5:

In Fig 11.17, write another name for:

(i) ∠1

(ii) ∠2

(iii) ∠3

(iv) ∠4

#### Answer:

(i) Another name for ∠1 is ∠BOD.

(ii) Another name for ∠2 is ∠BOC.

(iii) Another name for ∠3 is ∠AOC.

(iv) Another name for ∠4 is ∠ AOD.

#### Page No 11.6:

#### Question 6:

In fig. 11.18, Write another name for:

(i) ∠1

(ii) ∠2

(iii) ∠3

#### Answer:

(i) ∠BPE

(ii) ∠PQC

(iii) ∠DQF

#### Page No 11.6:

#### Question 7:

In Fig. 11.19, Which of the following statement are true:

(i) Point B is the interior of ∠AOB

(ii) Point B is the interior of ∠AOC

(iii) Point A is the interior of ∠AOD

(iv) Point C is the exterior of ∠AOB

(v) Point D si the exterior of ∠AOC

#### Answer:

(ii), (iv) and (v) are true statements.

(i) and (iii) are incorrect statements as B lies on ∠AOB and A lies on ∠AOD.

#### Page No 11.6:

#### Question 8:

Which of the following statements are true:

(i) The vertex of an angle lies in its interior.

(ii) The vertex of an angle lies in its exterior.

(iii) The vertex of an angle lies on it.

#### Answer:

(iii) The vertex of an angle lies on it.

This is the only correct statement.

#### Page No 11.6:

#### Question 9:

By simply looking at the pair of angles given in Fig. 11.20, state which of the angles in each of the pairs is greater:

#### Answer:

(i) ∠AOB is greater than ∠DEF.

(ii) ∠PQR is greater than ∠LMN.

(iii) ∠UVW is greater than ∠XYZ.

#### Page No 11.7:

#### Question 10:

By using tracing paper compare the angles in each of the pairs given in Fig. 11.21.

#### Answer:

Using tracing paper, we get that:

(i)∠PQR is greater than ∠AOB.

(ii) ∠UVW is greater than ∠LMN.

(iii) ∠RST is greater than ∠XYZ.

(iv) ∠PQR is greater than ∠EFG.

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