Even with trained operators and cooperative subjects, it is still possible to capture off-angle iris images. Considering the recent demands for stand-off iris biometric systems and the trend towards ”on-the-move-acquisition”, off-angle iris recognition became a hot topic within the biometrics community. In this work, CNNs trained with the triplet loss function are applied to extract features for iris recognition. To analyze which parts of the eye are most suited for the CNN-based recognition system, experiments are carried out using image data from different parts of the eye (full eye, eye zoomed to iris, iris only, iris normalized, eye without iris). To analyze the impact of different gaze angles on the recognition performance, experiments are applied on: (1) different gaze angles separately, (2) image data with increasing differences in the gaze angles, and (3) corrected off-angle image data. The experiment results show superior performance of the CNN trained with the triplet loss on the iris images with more lateral gaze angles 30°. However, higher differences in the gaze angles between images deteriorate the network performance. Also, the results are about the same for the different parts of the eye and correcting the gaze angle did not really improve the performance of the CNN.