We are tasked with finding the value of $x$ in the given geometric diagram.

Analysis:

• The horizontal line contains the $30^\circ$ and $x^\circ$ angles, which are supplementary angles, since they form a straight line. Therefore, we know: $30^\circ + x^\circ = 180^\circ$

• From this, we can solve for $x$: $x = 180^\circ - 30^\circ = 150^\circ$

Thus, the value of $x$ is $150^\circ$.

Would you like more details or have any questions?

Follow-up questions:

1. What are supplementary and complementary angles?
2. How are vertically opposite angles determined?
3. Can the exterior angle theorem be applied to this diagram?
4. What is the sum of angles in a triangle, and how does it relate here?
5. How do you calculate the interior angles of polygons?

Tip:

In problems involving straight lines, supplementary angles always add up to $180^\circ$.