Visual stimuli that entail the intersection of two or more straight lines elicit a variety of well known perceptual anomalies. Preeminent among these anomalies are the systematic overestimation of acute angles, the underestimation of obtuse angles, and the misperceptions of line orientation exemplified in the classical tilt, Zollner, and Hering illusions. Here we show that the probability distributions of the possible real-world sources of projected lines and angles derived from a range-image database of natural scenes accurately predict each of these perceptual peculiarities. These findings imply that the perception of angles and oriented lines is determined by the statistical relationship between geometrical stimuli and their physical sources in typical visual environments.