Determing "turning angle" of 3 points on a matrix

I am simulating movement of a bot on a matrix and keep track of its x and y coordinates. For every current position, I need to calculate the "turning angle" between the bot's current position and every possible new position (x,y coordinate) on the matrix that it can "move" to. I have attached a figure depicting what a turning angle is, but basically, it is the angle formed between the direction of the current movement and the new position. Let's say the red dot is (x1,y1), the blue dot is the current position (x2,y2), and the yellow dot is the potential new position (x3,y3). How can I determine this angle? I would need to find the angle for all possible new positions, but I can probably figure it out if I know how to do it for one.

Answer 1

[KSSV]

Use dot product.

theta = acos(dot(a,b)/(norm(a)*norm(b)) ;

where a and b are you position vectors.