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Angles in real life - class-IX

Description: angles in real life
Number of Questions: 27
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Tags: angle construction of angles lines and angles angles in our surroundings lines, angles and shapes angles complementary angle, supplementary angles and adjcent angles angles and triangles understanding elementary shapes shapes and angles basic geometrical concepts and shapes maths
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At 5'O clock the angle between two hands in a clock is 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. ${ 120 }^{ \circ }$

  2. ${ 130 }^{ \circ }$

  3. ${ 140 }^{ \circ }$

  4. ${ 150 }^{ \circ }$

Show answer
Correct Option: D
Explanation:
A clock has $12$ equal parts$={360}^{\circ}$
$1$ part$=\dfrac{{360}^{\circ}}{12}={30}^{\circ}$
At $5$O clock the hands will be between $12$ and $5=5$parts
$\therefore 5$ parts$=5\times{30}^{\circ}={150}^{\circ}$

The centre of a clock is taken as origin At 4.30 pm the equation of line along minute hand is x = 0 Therefore at this istant the equation of line along the hour hand will be 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $x - y = 0$

  2. $x + y = 0$

  3. $\displaystyle y=\sqrt{2x}$

  4. $\displaystyle y=\frac{x}{\sqrt{2}}$

Show answer
Correct Option: B
Explanation:

The centre of a clock is taken as origin. At 4:30 pm equation of line along minute hand is $x=0$.
Therefore at this instant the equation of line along the hour hand will be 
$m=-1$ ( as tan 135=-1 )
Therefore equation of line y=mx
or $y=-x$
$y+x=0$.

At 4.24 pm, how many degrees has the hour hand of a clock moved from its position at noon?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $132^\circ$

  2. $135^\circ$

  3. $140^\circ$

  4. $145^\circ$

Show answer
Correct Option: A
Explanation:

From noon 12 noon to 4:24 total minutes
4*60+24
=240+24
=264
Now in 12 hour angle made by the hour hand= $={ 360^0 } $
so in 1 minute angle made by the hour hand=360/12*60=$= { \frac { 1 }{ 2 }  } $
so in 264 minute angle made by the hour hand=$=264\times \frac { 1 }{ 2 } ={ 132^0 } $

The minute hand of a clock is 14 cm long
How much distance dose the end of the minute hand
travel in 15 minutes?$\displaystyle \left ( Take \pi  =\frac{22}{7}\right )$

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. 11 cm

  2. 22 cm

  3. 33 cm

  4. 44 cm

Show answer
Correct Option: B
Explanation:

Given minute hand of clock is 14 cm long

Then distance traveled by minute hand in 15 minutes
= one forth of circumference of circle radius 14 cm
=$\left ( \frac{1}{4}\times 2\times \frac{22}{7}\times 14 \right )=22 cm$

At 5:20 the angle formed between the two hands of a clock is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. obtuse

  2. right

  3. acute

  4. none of these

Show answer
Correct Option: C
Explanation:

A clock is a circle, and a circle always contains $360^o$. Since there are 


$60$ minutes on a clock, each minute mark is $6^o.$

$\Rightarrow$  $\dfrac{360^o}{60}=6\,degree$
The minute hand on the clock will point at $20$ minutes, allowing us to calculate it's position on the circle.

$\Rightarrow$  $20\,minutes\times 6=120\,degree$
So the angle made by the hour hand in $5$ hours $20$ minutes $= 5\dfrac{1}{3}hours$ 
                                                                                                    $=\dfrac{16}{3}\times\dfrac {360^o}{12}$ 
                                                                                                    $=160^o$

Hence angle between the hour hand and minute hand at $5:20=160^o-120^o=40^o$

$\therefore$  $40^o$ is less than $90^o$ means its acute angle.

$\therefore$   At $5:20$ the angle formed between the two hands of a clock is $acute.$

At 3 o'clock, the angle formed between the two hands of a clock is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. right

  2. acute

  3. obtuse

  4. left

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  A clock is a circle made of $360^o$. and that 

$\Rightarrow$  Each number represents an angle and the separation between them is $\dfrac{360}{12}=30^o$. 
$\Rightarrow$  At $2:00$, the minute hand is on the $12$ and the hour hand is on the $3$.  
$\Rightarrow$  The angle between two hands $=3\times 30^o=90^o$
$\Rightarrow$  At $3$ o'clock, the angle formed between the two hands of a clock is $right\,angle.$

At 9 o'clock the formed between the hands of a clock is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. complete angle

  2. reflex angle

  3. zero angle

  4. none

Show answer
Correct Option: D
Explanation:

At 9:00 the angle formed between the hands of a clock is a right angle..

At 3 o'clock the angle formed between the hands of a clock is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. reflex angle

  2. right angle

  3. straight angle

  4. acute angle

Show answer
Correct Option: B
Explanation:

At 3:00 the angle formed between the hands of clock is right angle..

Type of angle between the hands of a clock when the time is 5:20 is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. right angle

  2. straight angle

  3. obtuse angle

  4. acute angle

Show answer
Correct Option: D
Explanation:

It will form an acute angle..

An angle which measures $\displaystyle 180^{0}$  is called a

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. straight angle

  2. obtuse angle

  3. right angle

  4. complete angle

Show answer
Correct Option: A
Explanation:

Straight angle is a angle which measures 180 degrees..

Let $A$ be the angle between the minute and the hour hand at $6$ p.m. and $B$ be the angle between them at $12$ a.m. Then which of the following statements is true?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $A < B$

  2. $A > B$

  3. $A=B$

  4. None of these

Show answer
Correct Option: C

What is the angle between the hands of a clock, when they lie in a straight line ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $30^{o}$

  2. $60^{o}$

  3. $90^{o}$

  4. $180^{o}$

Show answer
Correct Option: D
Explanation:

When the hands of clock lie in straight line , a straight angle is formed.

Measure of straight angle $=180^{\circ}$
So option $D$ is correct.

What friction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $3$ to $9$

  2. $4$ to $7$

  3. $7$ to $10$

  4. $12$ to $9$

  5. $1$ to $10$

  6. $6$ to $3$

Show answer
Correct Option: A
Explanation:

Let us consider that for one hour the fraction of revolution is $\dfrac{1}{12}$

then :

(i)  $3$ to $9$ means $6$ hours

therefore; fraction of revolution $\dfrac{6}{12}=\dfrac{1}{2}$

(ii)  $4$ to $7$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$  

(iii)  $7$ to $10$ means $3$ hours

therefore; fraction of revolution $\dfrac{3}{12}=\dfrac{1}{4}$

(iv)  $12$ to $9$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(v)  $1$ to $10$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

(vi)  $6$ to $3$ means $9$ hours

therefore; fraction of revolution $\dfrac{9}{12}=\dfrac{3}{4}$

At what time between $2$ and $3$ the acute angle between the hour hand and the minute hand will be $50^{o}$

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $2:20$

  2. $2:25$

  3. $2:35$

  4. $2:40$

Show answer
Correct Option: A

The angle between the minute hand and the hour hand of a clock when the time is 3:30 in degree is

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. 90

  2. 09

  3. 88

  4. 75

Show answer
Correct Option: D
Explanation:
Angular speed of hour hand $= 30degree \,per\, hour. =0.5$ degree/minute.

In $30$ minutes , the angle swept by hour hand is $30\times 0.5 = 15$ degree.

At $3:30$ , the minute hand is at number $6$.

At $3:00$ the hour hand was at number $3$.

Now it has moved $15$ degree.

Hence the angle between the two is $\left(90 -15\right) = 75$ degree.

The angle between the minute hand and the hour hand of a clock when the time is 4:20 in degree is:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. 20

  2. 30

  3. 10

  4. 80

Show answer
Correct Option: C
Explanation:
The speed of hour hand is ( $30$ degree per hour) ${0.5}^{\circ}$ per minute.

The speed of minute hand is ($360$ degree per hour) ${6}^{\circ}$ per minute.

Relative to hour hand the speed of minute hand is $6-0.5 = {5.5}^{\circ}$per minute.

At $4$ O clock , hour hand is at $4$ and minute hand is at $12$.

Angle between them is ${120}^{\circ}$.

Keeping hour hand at $4$ , minute hand moves $20\times 5.5 = {110}^{\circ}$, in $20$ minutes.

Angle between them is ${120}^{\circ}-{110}^{\circ}={10}^{\circ}$.

At what time between 4 and 5, will the hands of a clock coincide?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. 15.81 min

  2. 21.81min

  3. 23.81 min

  4. 33.48 min

Show answer
Correct Option: B
Explanation:
We know minute hand of a clock covers ${360}^{\circ}$ in $60\ min$ or ${6}^{\circ}$ in $1$ minute and hour hand of a clock covers ${360}^{\circ}$ in $12\ hrs$ or ${30}^{\circ}$ in $1$ hour or $.5$ degree in $1$ min.

So at $4:00$ the minute hand has covered $0$ degrees and hour hand has covered $120$ degrees

Now let time after which these two coincide be $x$ min.

So hour hand covers $120+\dfrac{x}{2}$ upto that time and minute hand covers $6x$ degrees upto that time when they coincide the angles should be same

So, $120+\dfrac{x}{2}= 6x$

Solving we get $6x-\dfrac{x}{2}=120$

$\Rightarrow\,\dfrac{12x-x}{2}=120$

$\Rightarrow\,11x=240$

$\Rightarrow\,x=\dfrac{240}{11}$minutes

$\therefore\,x=21.81\ mins$

Angle between the minutes hand of a clock and hour hand when the time is 7 : 20 am is 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $\displaystyle 80^{\circ}$

  2. $\displaystyle 100^{\circ}$

  3. $\displaystyle 120^{\circ}$

  4. $\displaystyle 140^{\circ}$

Show answer
Correct Option: B

At $5:20$ the angle formed between the two hands of a clock is:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. obtuse angle

  2. right angle

  3. acute angle

  4. None of the above

Show answer
Correct Option: C
Explanation:

At $5:20$ the angle formed between the two hands of a clock will be less than $90^o$.

So, it is an acute angle.

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past $4$?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $\dfrac{\pi}{3}$

  2. $\dfrac{\pi}{4}$

  3. $\dfrac{\pi}{6}$

  4. None of the above

Show answer
Correct Option: B
Explanation:

In the clock the angle between each hour division will be $\dfrac { 360 }{ 12 } =30^{o}$. 

Now here at $4:30$, the hour hand will be along AB which is the angle bisector between $4$ and $5$ and the minute hand will be along AC,
The angle between them will be $=30+15=45$,in radians $\dfrac { \pi  }{ 4 }$ 

Hence, B is correct.

At what time is the angle between the hands of a clock equal to $30^{o}$ ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $1:00$

  2. $11:00$

  3. $2:00$

  4. $12:00$

Show answer
Correct Option: A,B
Explanation:

A clock is a circle made of $360^\circ$, and that each hour represents an angle and the separation between them is $\dfrac{360^\circ}{12}=30^\circ$


Hence, 
At $1:00$ the angle between the hands is $30^\circ$, minute hand pointing at 12 and hour hand at 1.

Similarly
At $11:00$ the angle between the hands is $30^\circ$

At $2:00$ the angle between the hands is $60^\circ$

At $12:00$ the angle between the hands is $0^\circ$

How many times between $6:00$ am and $6:00$ pm, do the hands of a clock make a straight line 

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $9$

  2. $10$

  3. $11$

  4. $12$

Show answer
Correct Option: C
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

 (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So between $6:00$ am to $6:00$ pm ($12$ hours), $11$ times hands of a clock make a straight line.

How many times in a day, do the hands of a clock make a right angle ?

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $21$

  2. $22$

  3. $42$

  4. $44$

Show answer
Correct Option: D
Explanation:

There will be $2$ times per hour when the angle between minute and hour hand is $90^\circ$

Total of $22$ times in $12$ hours.
$\therefore$ In $24$ hours, $22\times 2=44$ times the angle between minute and hour hand is $90^\circ$.

At 2:15 o'clock, the hour and minute hands of a clock form an angle of:

maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

  1. $30^{\circ}$

  2. $5^{\circ}$

  3. $22\dfrac{1}{2}{\circ}$

  4. $7\dfrac{1}{2}{\circ}$

Show answer
Correct Option: C
Explanation:
   $\underset { \downarrow  }{ \underline { 2 }  } <2:15<\underset { \downarrow  }{ 3 } $' $O$ clock
$\left( { 60 }^{ 0 } \right) $             $\left( { 90 }^{ 0 } \right) $
when minute hand rotates $15$ min hour hand rotate $\dfrac { 15 }{ 60 } \times { 30 }^{ 0 }={ 7.5 }^{ 0 }$
So, angle at $2:15$ is $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$

Angles are measured in

maths angles in our surroundings measuring and drawing angles angles in a clock checking angles between hands of a clock

  1. compasses

  2. protractor

  3. degrees

  4. centimetres

Show answer
Correct Option: C
Explanation:

Angles are measured in degrees

A circular paper is divided into $4$ equal parts by cutting it through two diameters. Then the central angle of each part is equal to:

maths angles in our surroundings measuring and drawing angles angles in a clock checking angles between hands of a clock

  1. $45^\circ$

  2. $90^\circ$

  3. $60^\circ$

  4. $30^\circ$

Show answer
Correct Option: B
Explanation:

Central angle $=360^{\circ}$

Now circular piece of paper is divided in four equal parts .
Let measure of central angle $=x$
$\ \Rightarrow x+x+x+x={ 360 }^{ \circ  }\ \Rightarrow 4x={ 360 }^{ \circ  }\ \Rightarrow x=\dfrac { { 360 }^{ \circ  } }{ 4 } \ \Rightarrow x={ 90 }^{ \circ  }$
So option $B$ is correct.

The central angle of a part of a circle which is divided into $6$ equal parts is:

maths angles in our surroundings measuring and drawing angles angles in a clock checking angles between hands of a clock

  1. $60^\circ$

  2. $30^\circ$

  3. $45^\circ$

  4. $90^\circ$

Show answer
Correct Option: A
Explanation:

Central angle $=360^{\circ}$

Now park is divided in four equal parts.

Let measure of central angle $=x$
$\ \Rightarrow x+x+x+x+x+x={ 360 }^{ \circ  }\ \Rightarrow 6x={ 360 }^{ \circ  }\ \Rightarrow x=\dfrac { { 360 }^{ \circ  } }{ 6 } \ \Rightarrow x={ 60 }^{ \circ  }$

So option $A$ is correct.

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