check the picture below.
let's keep in mind that there are 360° in a circular clock.
there are 12 numbers, so 12 even intervals, the angle between each interval, namely between each number is 360/12 , or 30°.
so between the tick at 8 and the tick at 9, that's 30°.
however, the minute hand has gone 15 minutes, only 1/4 of an hour, that means the hour hand has also moved 1/4 of the way from the tick at 8 towards the tick at 9.
from 3 to 9, as you see the red line there, is 180°, and now, let's subtract that tiny angle towards the green line.
the green line is 1/4 of the way, namely the hour hand has moved that much in 15 minutes, we know that between 8 and 9 is 30°, and we know the green line is 1/4 of the way towards 9, so the remaining part towards 9 has to be 3/4 of the way, namely 3/4 of 30°.
[tex]\bf \stackrel{\textit{the angle from 3 to 9}}{180^o}~~-~~\stackrel{\stackrel{\textit{the angle from 9 to 8}}{3/4~of~30^o}}{\left( \cfrac{3}{4} \right)30}\implies 180-22.5\implies 157.5^o[/tex]
