Why the vertical angles have the same measure?

Vertical angles are formed when two lines intersect, creating two pairs of opposite angles. The reason they have the same measure is due to the property of angles formed by intersecting lines: each pair of vertical angles is composed of two angles that are opposite each other, and they share the same vertex and are formed by the same pair of intersecting lines. Since the angles on a straight line sum up to 180 degrees, the pairs of vertical angles must also be equal. Thus, vertical angles are congruent.