measure angle between two lines, can rotation center constraint be used to refine the initial measured result?
You could recompute the lines with the constraint that they all go through the red point. If you normally optimize a line 

$$y=ax+b$$

by optimizing both parameters $a$ and $b$, you would now only have 1 degree of freedom for each line. If the red point has coordinates $(x_1,y_1)$ then you get
the constrained line equation

$$y=a(x-x_1)+y_1$$

with only one parameter $a$. Now you compute $a$ such that the squared distance to the other dots is minimized, and no matter which value of $a$ you obtain, the line will always pass through $(x_1,y_1)$.