  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. 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. 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. 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. 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.
