The magnetic polarities of bipolar active regions (ARs) exhibit elongations in line-of-sight magnetograms during their emergence. These elongations are referred to as magnetic tongues and attributed to the presence of twist in the emerging magnetic flux-ropes (FRs) that form ARs. Aims. The presence of magnetic tongues affects the measurement of any AR characteristic that depends on its magnetic flux distribution. The AR tilt-angle is one of them. We aim to develop a method to isolate and remove the flux associated with the tongues to determine the AR tilt-angle with as much precision as possible. Methods. As a first approach, we used a simple emergence model of a FR. This allowed us to develop and test our aim based on a method to remove the effects of magnetic tongues. Then, using the experience gained from the analysis of the model, we applied our method to photospheric observations of bipolar ARs that show clear magnetic tongues. Results. Using the developed procedure on the FR model, we can reduce the deviation in the tilt estimation by more than 60%. Next we illustrate the performance of the method with four examples of bipolar ARs selected for their large magnetic tongues. The new method efficiently removes the spurious rotation of the bipole. This correction is mostly independent of the method input parameters and significant since it is larger than all the estimated tilt errors. Conclusions. We have developed a method to isolate the magnetic flux associated with the FR core during the emergence of bipolar ARs. This allows us to compute the AR tilt-angle and its evolution as precisely as possible. We suggest that the high dispersion observed in the determination of AR tilt-angles in studies that massively compute them from line-of sight magnetograms can be partly due to the existence of magnetic tongues whose presence is not sufficiently acknowledged.