Find point B on line L given points AC where angle ABC equals angle X

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Trying to work out this tricky trigonometry question for a game I am programming. My maths knowledge is basic so if possible please keep the answer as basic as possible.

Need the formula to calculate point B on an infinite line L given two points AC where the angle ABC is equal to a specified angle X.

I understand also that there are normally two points with the specified angle X on the line L

So for example, if line L passed through points (0,10) and (10,0) and point A = (2,5) and point C = (5,2) and I wanted to find the target angle of 90 degrees then point B would be (5,5). Now, what if my target angle was 45 or 5 degrees what would point B be?

New image to illistate: Image

Thank you.