Sharp corner not smooth

[Mr. Start]

Hello i'm new to Illustrator and i'm starting to transform an art of mine to digital, but it seems i can't make the sharp edge the way i want with the pen tool, i'm trying to make as round as possible (Red line example), but it ended up like that ugly thing that go straight. Anybody has any tips?

Thanks!!

[Monika Gause]

That happens because of the automatic pointd corner Illustrator generated for the stroke. 

With that very small angle you cannot make it work automatically. You will have to either draw that as a shape or use the width tool to edit the stroke weight at the corner.

[Kurt Gold]

In the Strokes palette, take a look at the cap and corner options, as well as the miter limit setting.

[Ton Frederiks]

I would try the Round Join option in the expanded Stroke panel.