Tag: clock with respect to angles

Questions Related to clock with respect to angles

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 $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$