Question

Are vertical angles supplementary angles?

Answer 1

Vertical and supplementary are different relationships between angles.
However, there is a special case when vertical angles are supplementary as well - when these angles are right ones.

Explanation:

Vertical angles are formed by two intersecting lines. On a picture below angles `/_A` are vertical, as well as angles `/_B`.

Supplemental angles are those that, if positioned adjacent to each other, form a straight angle.
On a picture below angles `/_KML` and `/_KMH` are supplemental since together they form a straight angle `/_LMH`.

In one particular case, when vertical angles are right angles (that is, lines that form this pair of vertical angles are perpendicular), their sum is equal to a straight angles and, therefore, they are supplemental.
See the picture below that represents angles formed by perpendicular lines.
Angles `/_1` and `/_3` are vertical, as well as angles `/_2` and `/_4`. In addition, since lines are perpendicular to each other, all angles are congruent. Therefore, each of these pairs is also a pair of supplemental angles since their sum is a straight_ angle.