What is the smaller angle between the hour and minute hands at (2:40)?

Correct answer: (160^\circ)

The minute hand moves through six degrees each minute, so at 40 minutes it is at \\(40\\times6=240^\\circ\\) from 12. The hour hand does not remain exactly on the 2; it moves half a degree each minute. At 2:40 its position is \\(2\\times30+40\\times0.5=80^\\circ\\). The separation is therefore \\(240^\\circ-80^\\circ=160^\\circ\\). Since this is less than \\(180^\\circ\\), it is already the smaller angle. Hence option C, \\(160^\\circ\\), is correct.

A common mistake is to place the hour hand exactly at 2 and use only \\(60^\\circ\\), which would give the wrong result. The hour hand has advanced by 20 degrees during the 40 minutes, making its actual position 80 degrees. The minute hand is at 240 degrees, and the direct difference gives 160 degrees. No wraparound adjustment is needed because the difference is below 180 degrees. Thus, the supplied calculation and answer are consistent.