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Learn trigonometry and write a script that fills the gap for you (jk). You have to use plugins, unless if tnavarts improves snapping. Anyways use stravant’s gap fill, it’s the best and most accurate at the moment.
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Stop trying to be different and just use a plugin 
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To fill in that gap you’d actually need 2 wedges like so:
(Excuse me for my terrible drawing skills lol)
You’d just have to snap each wedge to the face of the part they’ll be facing… and from there you’ll have to simply adjust their size and find out where the two ends meet. Like the others have mentioned, you could use a plugin (which would probably save you a lot of time and effort), but if you still insist on doing it manually, that’s also fine.
Hope this helps!
Why don’t you wish to use the plugin?
Do you not trust them?
To figure out the triangle that fills the gap, I treated it as an isosceles triangle since both road parts are the same size and meet evenly at the pivot. The part width was 10.8 studs, and the rotation angle between them was 40°. To find the bottom gap (the triangle’s base), I used the Law of Cosines, which gave me a base of about 7.388 studs. Then, to find the triangle’s height from the base up to the top point, I used the Pythagorean theorem, which gave a height of about 10.149 studs.
That means the filler triangle should be about 7.39 studs wide and 10.15 studs tall to fit perfectly between the two rotated parts. (So two triangles 3.694 at the base)
This can be done with an isosceles triangle calculator
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It’s not that I don’t trust them, I just like knowing how things work because it is interesting, and don’t really want to rely on plugins all the time.
After having figured it out now, it seems that using the plugin will save WAY more time.
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