If two straight-lines, not lying on the same side,  make adjacent angles (whose sum is) equal to two right-angles  with some straight-line, at a point on it, then the two straight-lines will be straight-on (with respect) to one another. For let two straight-lines $BC$ and $BD$, not lying on the same side, make adjacent angles $ABC$ and $ABD$ (whose sum is) equal to two right-angles with some straight-line $AB$, at the point $B$ on it. I say that $BD$ is  straight-on with respect to $CB$. <prf> Thus, $CB$ is straight-on with respect to $BD$.Thus, if two straight-lines, not lying on the same side, make adjacent angles (whose sum is) equal to two right-angles with some straight-line, at a point on it, then the two straight-lines will be straight-on (with respect) to one another.