1. **State the problem:** We are given a triangle XYZ with angles labeled as $x + 2$, $2x + 23$, and $3x + 5$. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$ (x + 2) + (2x + 23) + (3x + 5) = 180 $$ 3. **Combine like terms:** $$ x + 2 + 2x + 23 + 3x + 5 = 180 $$ $$ (x + 2x + 3x) + (2 + 23 + 5) = 180 $$ $$ 6x + 30 = 180 $$ 4. **Solve for $x$:** $$ 6x = 180 - 30 $$ $$ 6x = 150 $$ $$ x = \frac{150}{6} $$ $$ x = 25 $$ 5. **Conclusion:** The value of $x$ is 25 degrees.