To solve for $x$ in the given triangle, we can use the following steps:

1. Use the Exterior Angle Theorem:

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the exterior angle is $143^\circ$, and the two non-adjacent interior angles are the right angle ($90^\circ$) and $x^\circ$.

Thus, we can write the equation: $143^\circ = 90^\circ + x^\circ$

2. Solve for $x$:

$x = 143^\circ - 90^\circ = 53^\circ$

So, the value of $x$ is $53^\circ$.

Summary:

The value of $x$ is $\boxed{53^\circ}$.

Would you like more details on any specific step or have any further questions? Here are 5 related questions to expand your understanding:

1. How does the Exterior Angle Theorem work in non-right triangles?
2. What is the sum of all interior angles of any triangle?
3. Can you explain how the exterior angle changes when a triangle is not right-angled?
4. How do we approach solving for missing angles if two angles are given?
5. What is the difference between exterior and interior angles in polygons?

Tip: When solving angle-related problems in triangles, remember that the sum of the interior angles of any triangle is always $180^\circ$.