We have two pairs of parallel lines, wich intersect by a given angle. We look for the coordinates of the intersection point of the inner lines, if we know the distances of the lines D1, D2 and the inclination of the second pair (alpha).

We find the inclination at the inner point in a similar triangle. This brings us to the solution for the coordinates (X/D1) and to the angle of the miter beta:



In case of alpha=90° or alpha=270° is  X=D2.