Question

The angle between the minute hand and hour hands of a clock at 8:30 os

Answer 1

Answer:

$\boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: = \: 75^{ \circ} \: }$

Step-by-step explanation:

We have to find the The angle between the minute hand and hour hand of a clock at 8:30.

We know,

$\sf \: Angle\:subtended\:by\:minute\:hand \: in \: 1 \: hour = {360}^{ \circ}$

So,

$\sf \: Angle\:subtended\:by\:minute\:hand \: in \: 60\: min = {360}^{ \circ}$

$\sf \: Angle\:subtended\:by\:minute\:hand \: in \:1\: min = {6}^{ \circ}$

$\sf \: Angle\:subtended\:by\:minute\:hand \: in \:30\: min = {180}^{ \circ}$

Now, Further, we know that

$\sf \: Angle\:subtended\:by\:hour\:hand \: in \:12\: hours = {360}^{ \circ}$

$\sf \: Angle\:subtended\:by\:hour\:hand \: in \:1\: hours = {30}^{ \circ}$

$\sf \: Angle\:subtended\:by\:hour\:hand \: in \:8 \dfrac{30}{60} (= 8 \dfrac{1}{2} = \dfrac{17}{2} ) \: hours = \dfrac{17}{2} \times {30}^{ \circ} = 255^{ \circ}$

Now,

$\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \:$

$\sf \: = \: 255^{ \circ} - 180^{ \circ}$

$\sf \: = \: 75^{ \circ}$

Hence,

$\implies\sf \: \boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: = \: 75^{ \circ} \: }$