If you are travelling in a
westerly direction in the Northern Hemsiphere, your
Great Circle Track angle will always decrease.
If you are travelling onwards from a GCT of 270°T, which is
what the question states, then your onward track will be LESS than 270°T, i.e.
South-Westerly. As you are now travelling in a southerly direction, your
latitude will of course be decreasing.