Step-by-step explanation:
when two lines intersect, 4 angles are formed. They create two pairs of nonadjacent angles. These pairs are called vertical angles.
now, the problem speaks about line segments. not endless lines.
with limited line segments some strange situations can occur, that could not happen with endless lines.
we cannot prove the statement, because there is already a counter example in the picture. so, the word "always" and therefore the whole statement is disproven.
the first picture did not prove or disprove anything, because these 2 line segments are not intersecting.
the second and the third picture show 2 intersecting line segments forming 2 pairs of equal, non-adjacent angles : vertical angles. so, all is ok here.
the fourth picture show 2 line segments that officially intersect, but the actually only touch each other at 1 point (O). so, they actually only form 2 angles : a smaller interior angle, and a larger exterior angle. together they describe a whole circle of 360° around O. but no 2 pairs of vertical angles.
so, this picture disproves it.