Question

Find the angle between the hour hand and the minute hand of a clock at
8:20 pm.

Answer 1

Answer:

$\boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: = \: 130^{ \circ} \: }$

Step-by-step explanation:

We have to find the The angle between the minute hand and hour hand of a clock at 8:20.

We know,

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

So,

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

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

$\sf \: Angle\:subtended\:by\:minute\:hand \: in \:20\: min = {120}^{ \circ}$

Now, Further, we know that

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

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

$\sf \: Angle\:subtended\:by\:hour\:hand \: in \:8 \dfrac{20}{60} = 8 \dfrac{1}{3} = \dfrac{25}{3} \: hours = \dfrac{25}{3} \times {30}^{ \circ} = 250^{ \circ}$

Now,

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

$\sf \: = \: 250^{ \circ} - 120^{ \circ}$

$\sf \: = \: 130^{ \circ}$

Hence,

$\implies\sf \: \boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: = \: 130^{ \circ} \: }$