No, vertical angles cannot be supplementary.
Vertical angles are the angles opposite each other when two lines intersect. They are formed when two lines cross and create two pairs of opposite angles. For example, if two lines intersect and form angles A, B, C, and D, then angle A is vertical to angle C, and angle B is vertical to angle D.
The key property of vertical angles is that they are always equal in measure. Therefore, if angle A is 50 degrees, angle C is also 50 degrees. Since supplementary angles are defined as two angles that add up to 180 degrees, the only way for vertical angles to be supplementary would be if they were both equal to 90 degrees. While that can happen, it is not a general rule.
In most cases, vertical angles are either both acute, both obtuse, or both right angles, but they will not sum to 180 degrees unless both happen to be right angles. Therefore, while certain specific situations may create supplementary vertical angles, they do not inherently have that relationship. In general, vertical angles cannot be supplementary.