Tag: angles in a clock

Questions Related to angles in a clock

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

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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. $180^{o}$

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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 $3$

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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. $2:40$

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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

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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

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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

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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. $\displaystyle 140^{\circ}$

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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

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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

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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.