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#### Question 1:

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

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.

#### Question 2:

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

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

#### 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

(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.

#### 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?

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.​

#### Question 5:

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

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

#### Question 6:

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

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.

#### Question 7:

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

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

#### 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?

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.

#### Question 9:

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

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˚

#### 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) $90{\frac{1}{2}}^{0}$

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.

#### Question 11:

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

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

#### 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

(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.

#### Question 13:

State the kind of each of the following angles:

(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˚.

#### Question 1:

The vertex of an angles lies

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

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

#### 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

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

#### 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

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

#### 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

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

#### 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

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

#### 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

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

#### Question 7:

An angle of measure 240° is

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

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

#### 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

(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°.

#### Question 9:

The number of degrees in 2 right angle is

(a) 90°
(b) 180°
(c) 270°
(d) 360°

(b) 180°

$\because$ 1 right angle = 90°

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

#### Question 10:

The number of degrees in $\frac{3}{2}$ right angles is
(a) 180°
(b) 360°
(c) 270°
(d) 90°

None of the options are correct.

$\because$ 1 right angle = 90°

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

#### 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°

(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°

#### Question 1:

Give three examples of angles from your environment.

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

#### Question 2:

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

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

#### Question 3:

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

(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.

#### 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.

(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.

#### Question 5:

In Fig 11.17, write another name for:

(i) ∠1
(ii) ∠2
(iii) ∠3
(iv) ∠4

(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.

#### Question 6:

In fig. 11.18, Write another name for:

(i) ∠1
(ii) ∠2
(iii) ∠3

(i) ∠BPE
(ii) ∠PQC
(iii) ∠DQF

#### 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

(ii), (iv) and (v) are true statements.
(i) and (iii) are incorrect statements as B lies on ∠AOB and A lies on ∠AOD.

#### 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.

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

#### 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:

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

#### Question 10:

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

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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