The image shows a pair of intersecting lines forming vertical angles. We are tasked with finding the value of $x$, where angles are expressed in terms of $x$ and $y$.

From the image, the angles are:

• $x^\circ$ and $10^\circ$ on one side (these are vertical angles).
• $5y^\circ$ and $10^\circ$ on the other side (these are also vertical angles).

We can set up the following relationships:

1. Since vertical angles are equal: $x^\circ = 10^\circ$ So, $x = 10$.

Let me know if you'd like further clarification, or if you have additional questions.

Related questions:

1. What are vertical angles and how are they related?
2. How do you determine the relationship between intersecting lines?
3. Can you explain alternate interior angles and their properties?
4. What is the difference between supplementary and complementary angles?
5. How can you solve for multiple variables in geometry problems?

Tip: When dealing with angles formed by intersecting lines, always remember that vertical angles are congruent (equal).