1. The Vertical Angle Theorem states that when two lines intersect, the pairs of opposite angles formed at the intersection are equal in measure. 2. To visualize this, imagine two lines crossing each other, creating four angles around the intersection point. The angles that are directly across from each other (called vertical angles) are congruent. 3. This happens because the intersecting lines create two pairs of adjacent angles that are supplementary, meaning their measures add up to 180 degrees. 4. Using this, if one angle is $x$, its adjacent angle is $180 - x$. 5. Since vertical angles share the same adjacent angle, they must be equal, so vertical angles are both $x$. 6. This theorem is fundamental in geometry and helps solve many problems involving angle measures without needing to measure them directly.