The image shows two intersecting lines, forming vertical (opposite) angles. Given one of the angles is $15^\circ$, the vertically opposite angle is also $15^\circ$ because vertical angles are always equal.

To find $x$, we use the fact that adjacent angles on a straight line add up to $180^\circ$:

$x + 15^\circ = 180^\circ$

Solving for $x$:

$x = 180^\circ - 15^\circ$

$x = 165^\circ$

Thus, the missing angle $x$ is $165^\circ$.

Would you like a step-by-step explanation in more detail? Here are five related questions to explore:

1. What is the vertical angles theorem, and why is it useful?
2. How can you find an unknown angle using the linear pair property?
3. What are complementary and supplementary angles?
4. How do intersecting lines form congruent angles?
5. Can two adjacent angles be equal if they form a straight line?

Tip:

When two lines intersect, always look for vertical and supplementary angles to quickly find missing angle measures.