greetings. i have tried so much math and research and i am certified going bananzas

I have 3 gui elements (or 3 GUI positions). The position of the red gui object C may be changed to any position. I am trying to find a formula to find the measure of the yellow angle in degrees (the angle between AB and AC) when C may be at any position in a 360* range around AB.

So it seems you want an angle, but Iâ€™m not sure if you want it signed, so Iâ€™ll give you both solutions.

Here is some magic code:

local aToB = (b.AbsolutePosition-a.AbsolutePosition).Unit
local aToC = (c.AbsolutePosition-a.AbsolutePosition).Unit
local closestAngle = math.acos(math.clamp(aToB:Dot(aToC), -1, 1))
local signedAngle = closestAngle * math.sign(Vector3.new(0,0,1):Dot(aToB:Cross(aToC)))

aToB is the unit vector going from a to b
aToC is the unit vector going from a to c
closestAngle is basically the angular distance between the two vectors (So the positive vector between them)
signedAngle is also the closest vector, but signed, meaning that it retains the information of the direction in which itâ€™s spinning (clockwise or counterclockwise)

Let me know if you have any questions c:<

EDIT: Iâ€™m also gonna plug here my VectorUtils, which is a library of math stuff Iâ€™ve build in the past 4 years. It contains the functions VectorUtils.AngleBetween(vector1, vector2) and VectorUtils.AngleBetweenSigned(vector1, vector2, axisOfRotation), which juuust so happen to be what you asked for.

Iâ€™ve figured something out! A major problem was that I was putting the equation in the Wrong Part Of The Code so it kept giving me errors or weird answers that didnâ€™t make sense and I assumed I was doing the math wrong

local AB = (script.Parent.Parent.B.AbsolutePosition - script.Parent.Parent.A.AbsolutePosition)
local AC = (script.Parent.Parent.C.AbsolutePosition - script.Parent.Parent.A.AbsolutePosition)
local angle = math.acos( (AB:Dot(AC)) / (AB.magnitude * AC.magnitude))

In the scenario described in the main post, this will get the angle between the two vectors in radians (unless Iâ€™m mistaken but it seems to be working from testing). The value will always be positive and below 180 degrees, so something else will have to be tacked on to find if C is positioned to the left or right of AB

Thank you so much for the help, Iâ€™ll definitely look at your library!