Welcome to Space stack exchange. This is a part of launch window analysis and I'd recommend using that as a search term.
The simplest answer is "a bit more than 180 degrees". This is for the situation where the launch site is on the equator and the target satellite is geostationary rather than inclined geosynchronous orbit. Imagine that the launcher puts the chasing satellite directly into an elliptical GTO. It will take a little while for the launcher to get to perigee velocity/height. Then the chasing satellite has its perigee a little to the East of the launch site ( this accounts for the "bit") and its apogee is 180 degrees around the globe (that's your "180" degrees, funnily enough).
In any case one would probably make an allowance for a near GEO drift orbit. That is to say that if the GTO-GEO apogee kick deliberately targets a non GEO radius then the resulting orbit will have an East or West drift to it. One might choose to do this deliberately to account for launcher performance uncertainty, to check out the chaser satellite prior to arrival or just because the target isn't at the ideal longitude that is the subject of the OP.
A more complex examples is where the launch site is not on the equator. The GTO will now be inclined and thus its perigee can no longer be freely chosen to be "a little to the East of the launch site". Instead the perigee sensibly needs to be close to the equator (i.e. the nodal crossing) to get an efficient (geometrical) combination of performing the apogee kick and the inclination reduction at the same point. This means that the perigee/node crossing point may well be quite a long way East of the launch site, the higher the latitude the further it will be. That could add up to 90 degrees to the simple case of "a bit more than 180 degrees".
Lastly, given its the morning here and I haven't had a coffee yet, if the target satellite is itself inclined then the manoeuvres for apogee kick and the inclination reduction have the opportunity to do a "node shift" which in human terms means to change the inclination achieved in the GTO orbit to one which lines up with the target inclined orbit.