the story of the hour hand and the minute hand

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

$[9(60)+20](0.5) = 280^\circ$

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

$20(6)=120^\circ$

Therefore, the smaller angle formed is $280-120=160^\circ$ and the bigger angle formed is $360-160=\boxed{200^\circ}$