1. **State the problem:** We are given the equation $x + 38 + 90 = 180$ and need to solve for $x$. 2. **Use the angle sum property of a triangle:** The sum of the interior angles of a triangle is always $180$ degrees. This is the formula we use: $$x + 38 + 90 = 180$$ 3. **Simplify the equation:** Combine the known angles: $$x + 128 = 180$$ 4. **Isolate $x$:** Subtract $128$ from both sides: $$x + \cancel{128} - \cancel{128} = 180 - 128$$ $$x = 52$$ 5. **Interpretation:** The unknown angle $x$ measures $52$ degrees. This completes the solution for the first problem.