Question

Find the angle measure between the hands of the clock in each figure :

Answer 1

We know that when the hours hands complete one full rotation it completes $12$ hours or ${360}^{\circ }$

Hence, we can say that,

$\Rightarrow 12hr={360}^{\circ }$

$\therefore 1hr={30}^{\circ }$

(a) Since from $9$ to $12$, there are $3$ hours. Thus, to complete these $3$ hours, hour hand has to move a particular angle which will give us the angle between the hour hand and the minute hand.

$\therefore 3hr=3\times {30}^{\circ }={90}^{\circ }$

Thus, angle between the hands is ${90}^{\circ }$

(b) There is $1$ hour between the hands of the clock. Therefore, the required angles is,

$\Rightarrow 1hr={30}^{\circ }$

(c) There are $6$ hours between the hands of the clock. Therefore, the required angles is,

$\Rightarrow 6hr=6\times {30}^{\circ }={180}^{\circ }$