**Chapter 11: Angles Exercise 11.2**

**Question: 1**

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

**Solution:**

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.

**Question: 2**

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

**Solution:**

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

**Question: 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.

**Solution:**

(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?

**Solution:**

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.

**Question: 5**

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

**Solution:**

If the 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?

**Solution:**

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.

**Question: 7**

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

**Solution:**

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 × 4.5) = 18 right angles.

**Question: 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?

**Solution:**

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.

**Solution:**

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

Therefore, angle between any two adjacent spokes = 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^{↑8}

(vi) 75^{°}

(vii) 180^{°}

(viii) 89.5^{°}

(ix) 30^{°}

(x) 90^{°}

(xi) 179^{°}

(xii) 360^{°}

(xiii) 90.5^{°}

**Solution:**

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.

**Question: 11**

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

**Solution:**

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

**Solution:**

(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:

**Solution:**

(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:

**Question: 1**

The vertex of an angle lies

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

**Solution:**

(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

**Solution:**

(c) an angle.

An angle is a figure 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

**Solution:**

(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

**Solution:**

(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

**Solution:**

(c) a straight angle.

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

**Question: 6**

An angle of measure 360^{°} is called

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

**Solution:**

(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

**Solution:**

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.

**Solution:**

(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 angles is

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

**Solution:**

(b) 180^{°}

Since, 1 right angle = 90^{°}

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

**Question: 10**

The number of degrees in 3/2 right angles is

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

**Solution:**

None of the options are correct.

The correct answer is 135^{°}

Since, 1 right angle = 90^{°}

Therefore, 3/2 right angles = 3/2 x 90°^{ }= 135^{°}

**Question: 11**

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

(a) 10^{°} (b) 15^{°} (c) 20^{°} (d) 12^{°}

**Solution:**

(a) 10^{°}

The complete angle of bicycle wheel measures is 360^{°}.

Therefore, the angle between two adjacent spokes of the containing 36 spokes = 360/36 = 10^{°}.