To find the size of angle $x$ in this triangle, we will use some basic geometry.

Step-by-step approach:

1. Angle sum property of a triangle: In any triangle, the sum of the interior angles equals $180^\circ$. Therefore, the sum of the given angle $33^\circ$, the unknown angle $x$, and the right angle (which is $90^\circ$) must be equal to $180^\circ$.

   $33^\circ + x + 90^\circ = 180^\circ$

2. Solve for $x$: $x = 180^\circ - 33^\circ - 90^\circ$ $x = 57^\circ$

So, the size of angle $x$ is $57^\circ$ to the nearest integer.

Would you like any further details or clarification?

Here are 5 related questions you may find interesting:

1. How do you apply the Law of Sines in a triangle?
2. What is the difference between an acute and obtuse angle?
3. How do you calculate the area of a triangle?
4. Can this triangle be classified as a right triangle?
5. How do you solve for missing sides in a triangle using trigonometric ratios?

Tip: Always remember that the sum of angles in any triangle will always be $180^\circ$. This is a fundamental property that helps with many triangle-related problems.