Shifting Angel placement

First of all, thank you all developers for an excellent instrument, I love GeoGebra.

Trying to show (visualizing) that the surface of the Sperical triangle match the surplus angle (r=1)

by moving the point to some extreme location as the equator.

Everything goes well until I try to put out the angles between resp. tangent.

I want the inner (Blue-ish) angel to show, not the other angle (Black-ish).

As it is now I have to calculate them witch is easy but not so neat, I think.

Question: Is there any way to decide exatly where the angles are placed, and make them stay there?

problem and tries:

I understand that its possible to put a segment or point along the tangents and

force the angle to attach to them but that too is not very nice.

And even so these angles will change position as angles shifts past 180 deg. limit

giving totaly wrong angle to calulate with.

Trying both segments and points attached to the tangent was not very succesfull either as both Line

and point are moved along the tangent in opposit direction when I move the point (C) and the program decide to show wrong angle.

Further more when shifting direction along the tangent the point and segment will get such a

large value that it is hard to restore it have to zoom out and drag it back.

Changing back the point (C) will only rearly restore the angle at it proper place.

In contrast the other angle θ_{C} and its fellows (Black-ish) in the figure are very stable and good to use in calculation.

I cant find any way to make the angle stay put in their place as they have to be locked to the tangents.

One could live the the fact that one has to do a 180 - angle calculation to get the proper value but it would be nicer if we could view it direcly.

If there are no way to do this I can stop trying and clean up the figure from all test - debris.

https://ggbm.at/pGEtBRea