What is the minimum angle off horizontal before a line visually appears inclined at first glance? Here is a straight line, which visually looks like a straight line:



At first look (lets say minimum 2–3 sec.) the line below looks straight, but after some time you can see that it is actually an inclined line. You need some time (more then 5–8 sec.) to classify that line as a inclined line.



Here is an inclined line, which looks like an inclined line at first look:


Question: Is there any study that determines the minimum angle at which a line should be inclined to be visually classified at first look as an inclined line?
Vogels and Orban (1985) asked subjects to complete several thousand angle judgments at near-principal angles (horizontal or vertical). They found that the just-noticeable difference (JND), the threshold at which people could reliably detect deviation from a horizontal line, was 0.5 degrees after a 600ms exposure to the stimulus.

The real purpose of their study was to compare learning effects for judgments of deviations from principal orientations with judgments of deviations from oblique (diagonal) angles. They found that while people could double their sensitivity over extensive training to small changes in oblique angles, the principal angles showed no such learning effects, as you can see in this graph:



Additionally, the threshold for detection of changes from principal angles was about twice as good as the oblique angles, even after 5000 trials of practice discriminating oblique angles. 

Reference

Vogels, R., &amp; Orban, G. A. (1985). The effect of practice on the oblique effect in line orientation judgments. Vision research, 25(11), 1679-1687.