To solve for $x$ in the triangle where the given angles are $42^\circ$ and a right angle ($90^\circ$), we use the following property:

Property of a Triangle:

The sum of the internal angles of any triangle equals $180^\circ$.

Steps to Solve:

1. Identify the known angles:

   • $42^\circ$ (one angle),
   • $90^\circ$ (right angle),
   • $x$ is the unknown angle.

2. Set up the equation: $42^\circ + 90^\circ + x = 180^\circ$

3. Simplify the equation: $132^\circ + x = 180^\circ$

4. Solve for $x$: $x = 180^\circ - 132^\circ$ $x = 48^\circ$

Final Answer:

The measure of angle $x$ is $48^\circ$.

Do you want a detailed explanation of how the angles in a triangle add up to $180^\circ$, or do you have further questions?

Here are 5 related questions to expand your understanding:

1. How can you determine the missing angle in any triangle?
2. Why do the angles of a triangle always add up to $180^\circ$?
3. How do you solve for missing angles in non-right triangles?
4. What is the sum of the angles in a quadrilateral?
5. How can you use trigonometry to solve for sides and angles in right triangles?

Tip: Always remember that in a right triangle, one angle is always $90^\circ$, and the other two must sum up to $90^\circ$.