angle in the given time - 2

With reference to $12$ , the hour hand travels $0.5^\circ$ per minute, so it travelled

$[11(60)+45](0.5) = 352.5^\circ$

With reference to $12$ , the minute hand travels $6^\circ$ per minute, so it travelled

$45(6)=270^\circ$

Therefore, the smaller angle formed is $352.5-270=82.5^\circ$ and the bigger angle formed is $360-82.5=277.5^\circ$ .

Thus, the difference between them is $277.5-82.5=\boxed{195^\circ}$