Tag: angles in a clock

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Questions Related to angles in a clock

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

At 5'O clock the angle between two hands in a clock is 

  1. ${ 120 }^{ \circ }$
  2. ${ 130 }^{ \circ }$
  3. ${ 140 }^{ \circ }$
  4. ${ 150 }^{ \circ }$
Reveal answer Fill a bubble to check yourself
D Correct answer
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$=5\times{30}^{\circ}={150}^{\circ}$
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

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 

  1. $x - y = 0$
  2. $x + y = 0$
  3. $\displaystyle y=\sqrt{2x}$
  4. $\displaystyle y=\frac{x}{\sqrt{2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $y=-x$
$y+x=0$.

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

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

  1. $132^\circ$
  2. $135^\circ$
  3. $140^\circ$
  4. $145^\circ$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 } $

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

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

  1. 11 cm

  2. 22 cm

  3. 33 cm

  4. 44 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
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
=$\left ( \frac{1}{4}\times 2\times \frac{22}{7}\times 14 \right )=22 cm$

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

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

  1. obtuse

  2. right

  3. acute

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $acute.$

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

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

  1. right

  2. acute

  3. obtuse

  4. left
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $right\,angle.$