1. **State the problem:** We have a right triangle with one angle of 48° and sides of 19 cm (opposite to angle 48°) and 24 cm (adjacent to angle 48°). We need to find the unknown angle $x^\circ$. 2. **Recall the triangle angle sum rule:** The sum of angles in any triangle is 180°. Since one angle is 90° (right angle) and another is 48°, the third angle $x$ can be found by: $$x = 180^\circ - 90^\circ - 48^\circ$$ 3. **Calculate $x$:** $$x = 180^\circ - 138^\circ = 42^\circ$$ 4. **Answer:** The unknown angle $x$ is $42^\circ$. This method uses the fundamental property of triangle angles without needing side lengths for this part.