Determining the angle between a line x = n(1, ....) and an angle bisector.

[bogo]

Hello all, I'm working on a coding project where I'm trying to determine the deviation in degrees from a line X = B.x2 at a point B(x2,y2) by another line formed by bisection of the angle ABC of A(x1,y1), B(x2,y2) and C(x3,y3) : check the image below, it's more clear:




with the help of a friend I've managed to write some pseudo code and a sample python code for the case when B is always above A and C as follows:

English pseudo code in reference to the image above:

if B is above A and C then:
   BA|x| = B.x - A.x   //magnitude of x
   BA|y| = B.y - A.y  // " y

   BC|x| = B.x - C.x  // " x
   BC|y| = B.y - C.y // " y

 
   angle_alpha = tan^-1( BAy / BAx )) // angle between AB and line y= B.y
   angle_beta  = tan^-1( BCy / BCx )) // angle between AC and line y= B.y

   angle_gamma = 90 - angle_alpha      //angle between line BA and line x=B.x
   angle_delta = 90 - angle_beta       //angle between line BC and line x=B.x
 
   angle_omega = angle_gamma + angle_delta //angle between BA and BC
   bisected_angle = angle_omega/2          //angle between Z and BA or BC
 
   // next we determine the quadrant our bisector lies in as the points in some
   //instances Z can be on the left of Q

   if angle_delta is greater than angle_gamma then:
     our_quadrant = fourth //// between 270 && 360 degrees
     angle_theta  = bisected_angle - angle_delta

   otherwise:
     our_quadrant = third // between 180 && 270 degrees4
     angle_theta  = bisected_angle - angle_gamma

   we return our quadrant & angle_theta

sample python code:

import math

def error_angle(A, B, C):
    # Calculate BA and BC vectors
    BAx = B[0] - A[0]
    BAy = B[1] - A[1]
    BCx = B[0] - C[0]
    BCy = B[1] - C[1]
 
    # Calculate angles alpha and beta
    angle_alpha = math.degrees(math.atan(BAy/ BAx))
    angle_beta = math.degrees(math.atan(BCy/ BCx))
 
    # Calculate angles gamma and delta
    angle_gamma = 90 - angle_alpha
    angle_delta = 90 - angle_beta
 
    # Calculate angle omega (angle between BA and BC)
    angle_omega = angle_gamma + angle_delta
 
    # Calculate the bisected angle
    bisected_angle = angle_omega / 2
 
    # Determine the quadrant
    if angle_delta > angle_gamma:
        our_quadrant = "fourth"
        angle_theta = bisected_angle - angle_delta
    else:
        our_quadrant = "third"
        angle_theta = bisected_angle - angle_gamma
 
    return our_quadrant, angle_theta

# Example usage
A = (2, 4)
B = (5, 8)
C = (8, 2)
quadrant, angle = error_angle(A, B, C)
print("Quadrant:", quadrant)
print("Angle:", angle)

I'd really appreciate if someone could check if my logic is accurate and also how would I handle the case where B is below A and C where theta could lie in either quadrant 1(0-90 degrees) or quadrant 2(90-180 degrees)... only these two cases need to be handled.

 

[bogo]

Additional info: