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Checking angles between hands of a clock - class-VIII

Description: checking angles between hands of a clock
Number of Questions: 24
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Tags: maths angle angles and triangles understanding elementary shapes angles complementary angle, supplementary angles and adjcent angles shapes and angles lines and angles construction of angles
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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 $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$
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