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°.