Artificial intelligence (AI) has proven very useful in dental applications in recent years. The automatic extraction of information from X-ray panoramic dental radiographs represents an opportunity to streamline dental diagnosis and improve the precision of detecting oral pathologies. In particular, deep learning (DL) algorithms based on convolutional neural networks (CNNs) have demonstrated high performance in dental image classification, detection, and segmentation applications. However, several challenges remain due to the high variability of categories in dental applications. To characterize four different third molars angles employing X-ray panoramic radiographs, we focused on using the CNN-based object detection technique You Only Look Once (YOLO), which works with the GoogleNet feature extractor CNN. For this, we applied Winter's classification criterion, which describes the position of the third molars with respect to the longitudinal axis of the second molar. Third molar angles were divided into different categories: distoangular, vertical, mesioangular, and horizontal. A total of 644 panoramic X-ray images were used to train the YOLO algorithm. The proposed model reached an average accuracy performance of up to 97% on the test dataset. These findings exhibit the potential and reassuring results of employing CNNs for dental applications, specifically for object detection in panoramic X-rays.