This paper details a new automatic calibration method for the boresight angles between a LiDAR (Light Detection and Ranging) and an inertial measurement unit (IMU), based on a data selection algorithm, followed by the adjustment of boresight angles. This method, called LiDAR-IMU boresight automatic calibration (LIBAC), takes in input overlapping survey strips following simple line patterns over regular slopes. We first construct a boresight error observability criterion, used to select automatically the most sensitive points to boresight errors. From these points, we adjust the boresight angles. From a statistical analysis of the adjustment results, we derive the boresight angle precision. Results obtained with LIBAC on several LiDAR system integrated within drones are presented. We also give results about the reproducibility of the method.