We previously found that surprisingly many V2 neurons showed selective responses to particular angles embedded within continuous contours [M. Ito & H. Komatsu (2004)Journal of Neuroscience, 24, 3313–3324]. Here, we addressed whether the selectivity is dependent on the presence of individual constituent components or on the unique combination of these components. To reveal roles of constituent half-lines in response to whole angles, we conducted a quantitative model study after the framework of cascade models. Our linear–non-linear summation model implemented a few subunits selective to particular half-lines and was fitted to neuronal responses for each neuron. The study indicates that the best-fitting models well replicate the selectivity in the majority of V2 neurons and that the angle selectivity is dependent on a linear combination of responses to individual half-line components of the angles. The implication is that optimal angles are given by a combination of two preferred half-line components and the selectivity is sharpened by introducing suppression to non-preferred half-line components, rather than a specific facilitatory interaction between two preferred half-line components. The study indicates the participation of the gain control of responsiveness according to the number of half-line components. We also showed that the selectivity to acute angles depends on a combination of responses to one preferred component and weak responses to another component. Therefore, we concluded that the angle selectivity is dependent on selective responses to individual half-line components of the angles rather than a unique combination between them, whereas neurons could be selective to various angle widths at area V2.