The image shows two intersecting lines that form vertically opposite angles. One angle is given as $51^\circ$, and the other angle is labeled as $x$. Since vertically opposite angles are equal, the missing angle $x$ can be determined easily.

Solution:

Since vertically opposite angles are equal:

$x = 51^\circ$

So, the missing angle $x$ is $51^\circ$.

Would you like any more details or have any questions?

Related Questions:

1. What are vertically opposite angles?
2. How can you find angles when lines intersect at different points?
3. What are the properties of supplementary angles?
4. How can you find missing angles in parallel lines cut by a transversal?
5. What are adjacent angles, and how do they relate to intersecting lines?

Tip:

When two lines intersect, always remember that vertically opposite angles are equal, and adjacent angles add up to $180^\circ$.