Question on intersecting paths/ tapering

Hello all,
I have a question that I cannot seem to solve and I figured this would be the perfect place to ask. I am pretty knowledgeable in Illustrator, but I am self taught so there may be some things I have missed along the way and this is one that is bugging the heck out of me.
When creating a vector image from scratch and using the path tools I am running into a problem of cleanliness when intersecting paths and adding lines to preexisting paths....
Here is an image to demonstrate my frustration...
I need advise on how to keep lines like this clean? Can I taper the end of paths? is there a way to erase the stray end? How to I change the angle of the end of the path? Any help to this solution would be beneficial.
Thanks!

enorthem,
So essentially you think the easiest thing to do for that angle is to
create two separate paths parallel and butted up against each other to
imitate the desired thickness?
It would be easier to Object>Path>Outline Stroke as suggested by Monika in the first post. My path doubling suggestion was a way to avoid outlining and creating the transition with stroked paths only.
You can do as follows to get precisely fitting/matching double, or even triple, paths with overlapping to avoid gaps:
For a double path:
1) Create the upper/lower path with a Stroke Weight that is bit more than half the intended apparent thickness and a length that is a bit extensive;
2) Object>Path>Offset Path with a value that equals the difference between the intended apparent thickness and the Stroke Weight;
3) With the Scissors Tool cut the offset path at the ends of the part to be used, and delete the rest;
4) Adjust the lengths by clicking with the Scissors Tool and snipping off the surplus as needed.
For a triple path:
1) Create the central path with a  Stroke Weight that is bit more than one third the intended apparent thickness  and a length that is a bit extensive;
2) Object>Path>Offset  Path with a value that equals half the difference between the intended  apparent thickness and the Stroke Weight;
3) With the Scissors Tool cut the offset path at the ends of both the parts to be used, and delete the rest (the short straight segments in between);
4) Adjust the lengths by clicking with the Scissors Tool and snipping off the surplus as needed.
what would make this easier would be if there was a way to add a point
to one path and have it extend horizontally to a completely different
path, but correct me if I'm wrong, I don't think that is possible.
Nothing to correct.

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