So I was writing a solution to a problem, and I noticed that it would be unnecessary to add the point of intersection between two lines (say $\ell_1$ and $\ell_2$) to just represent the angle formed between them. So instead I thought about using the notation $\angle(\ell_1,\ell_2)$.
Till now, I knew that $\angle(\ell_1,\ell_2)$ represents the acute angle between the two lines, but the renouned geometry diagram making software, GeoGebra, seems to contradict this idea.
The way GeoGebra seems to define the angles is that if you have $\angle(\ell_1,\ell_2)$, then it's value will be the angle that $\ell_1$ needs to be rotated in an anti-clockwise direction at the intersection point to map to $\ell_2$, and alongside keeping in mind the orientation (that is if $\ell_2$ runs from left to right, then after rotating $\ell_1$ through their intersection point, we must have that the final image of $\ell_1$ runs in a left to right direction too).
Another doubt of mine is that if $\angle(\ell_1,\ell_2)$ actually represented the value of the acute angle between the two lines, then it seems that there is no purpose of defining the directed angles between two lines, which is represented as $\measuredangle(\ell_1,\ell_2)$.
I have also attatched a few screenshots for the verification.
