11 to 11.40 is 40 minutes. So if the minute hand moves 60 in 10 minutes, it would move 240 in 40 minutes.
The angle between 11 and 11.30 is 180 degrees.
The angle between 11.30 and 11.40 is 10 minutes, so the angel is 60 degrees, the same as the first bit of information in the quesiton.