The measure of vertically opposite angles formed by intersecting lines is always equal.

When two lines intersect, they create two pairs of vertically opposite angles that are always equal to one another. This property is consistent whether the lines are parallel or not. However, in the context of parallel lines, this concept is often complemented by other angle relationships, such as corresponding angles, alternate interior angles, and co-interior angles.

To visualize this, consider two parallel lines that are intersected by a transversal—a line that crosses both parallel lines. At the points where the transversal intersects the parallel lines, several angles are formed. For example, if the transversal intersects the parallel lines at points $A$ and $B$, the angles created at these intersections will include pairs of vertically opposite angles. This means that if one angle at point $A$ measures $50^\circ$, then the angle directly opposite it at the same intersection will also measure $50^\circ$.

Understanding vertically opposite angles is essential for solving many geometric problems, particularly those involving parallel lines and transversals. This knowledge aids in calculating unknown angles and in proving the parallelism of certain lines. The key takeaway is that vertically opposite angles are always equal, providing a dependable tool for analyzing geometric figures.