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#### Page No 11.10:

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:

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

#### Page No 11.10:

(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:

The measure of the angle between:
(i) North and west is 90o.​
(ii) North and South is 180o.​
(iii) North and South-East is 135o.​

#### Page No 11.10:

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:

After making a quarter turn or a turn of 90o,​ 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:

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

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

$\frac{360˚}{90˚}$ = 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:

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 × 4 = 10 right angles.

#### Page No 11.10:

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

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

#### Page No 11.10:

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$\frac{1}{2}$° is an obtuse angle.

#### Page No 11.10:

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

#### Page No 11.10:

(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.

#### Page No 11.11:

(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˚.

#### Page No 11.11:

(c) on the angle
The vertex of an angle lies on the angle.

#### Page No 11.11:

(c) an angle
An angle is a figure formed by two rays with the same initial point.

#### Page No 11.11:

(d) None of these
An angle of measure 0° is called a zero angle.

#### Page No 11.11:

(b) a right angle
An angle of measure 90° is called a right angle.

#### Page No 11.11:

(c) a straight angle
An angle of measure 180° is called a straight angle.

#### Page No 11.12:

(d) a complete angle
An angle of measure 360° is called a complete angle.

#### Page No 11.12:

None of the given options are correct.
An angle of measure 240° is called a reflex angle.

#### Page No 11.12:

(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:

(b) 180°

$\because$ 1 right angle = 90°

$\therefore$ 2 right angles = 90°​ × 2 = 180°

#### Page No 11.12:

None of the options are correct.

$\because$ 1 right angle = 90°

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

#### Page No 11.12:

(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:

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:

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

#### Page No 11.5:

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

#### Page No 11.6:

(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:

(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.

(i) ∠BPE
(ii) ∠PQC
(iii) ∠DQF

#### Page No 11.6:

(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:

(iii) The vertex of an angle lies on it.
This is the only correct statement.

#### Page No 11.6:

(i) ∠AOB is greater than ∠DEF.
(ii) ∠PQR is greater than ∠LMN.
(iii) ∠UVW is greater than ∠XYZ.

#### Page No 11.7:

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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