We investigated the angular resolution subserving the haptic perception of raised-line drawings by measuring how accurately observers could discriminate between two angle sizes under various conditions. We found that, for acute angles, discrimination performance is highly dependent on exploration strategy: mean thresholds of 2.9° and 6.0° were found for two different exploration strategies. For one of the strategies we found that discriminability is not dependent on the bisector orientation of the angle. Furthermore, we found that thresholds almost double when the angular extent is increased from 20° to 135°. We also found that local apex information has a significant influence on discrimination for acute as well as obtuse angles. In the last experiment we investigated the influence of depiction mode but did not find any effect. Overall, the results tell us that the acuity with which angles in raised-line drawings are perceived is determined by the exploration strategy, local apex information, and global angular extent.