How to properly sharpen concave angle without affecting topology? Here I have this shape with 2 concave angles and I want to sharpen them without affecting the surrounding loops.
I dont want to use crease or edge split because it create a 100% sharp edge which I dont want.
It seems you are using modifiers: Solidify and Subsurf.

The problem here, is that you don't have any real edge to apply crease.

First you should apply the Solidify Modifier, then you could get the edge in the red circle you drawn.

The crease amount will influence the shape, from completly smooth to completly sharp.

Alternatively, you could select the edge and apply a Bevel.

Select the edge, W, Bevel



Set the amount and the other properties in the panel (T)