Angle between hands

$\text{total angle=360 degree}$

$\text{so,for each hour there is =30 degree}$ .........[12 hours in a full rotation]

$\text{so,for each minute there is=6 degree}$ .........[60 minutes in a full rotation]

now, for $2:18$

the difference between minutes dial and hours dial is 8.

so,there has been created $8 \times 6 degrees=48 degrees$

but ,the hour hand of the watch has moved a bit between this 18 minutes.so,there will be less than 48 degrees.

now, for 18 minutes, the hour hand has moved 3.6 steps.if we consider the move from 2 it will be=1.6 steps.

as for 1 step, it crosses 6 degrees.so, for 1.5 steps, it will cross 9 degrees.

now, the total angle inner angle in $2:18$ is= $48-9=39 degrees$

$\text{believe me,i did it within 15 seconds in my mind.}$