From J.M.'s comment:
lineLineAngle[Line[{X1_, X2_}], Line[{X3_, X4_}]] := VectorAngle[Abs[X1VectorAngle[X1 - X2]X2, Abs[X4X4 - X3]];X3]
example:
line1 = Line@RandomReal[{0, 1}, {2, 2}];
line2 = Line@RandomReal[{0, 1}, {2, 2}];
lineLineAngle[line1, line2]
From J.M.'s comment:
lineLineAngle[Line[{X1_, X2_}, {X3_, X4_}]] := VectorAngle[Abs[X1 - X2], Abs[X4 - X3]];
From J.M.'s comment:
lineLineAngle[Line[{X1_, X2_}], Line[{X3_, X4_}]] := VectorAngle[X1 - X2, X4 - X3]
example:
line1 = Line@RandomReal[{0, 1}, {2, 2}];
line2 = Line@RandomReal[{0, 1}, {2, 2}];
lineLineAngle[line1, line2]
From J.M.'s comment:
lineLineAngle[Line[{X1_, X2_}, {X3_, X4_}]] := VectorAngle[Abs[X1 - X2], Abs[X4 - X3]];