1. **State the problem:** We are given two adjacent angles on a straight line: one angle is $(x + 2)^\circ$ and the other is $57^\circ$. We need to find the value of $x$. 2. **Formula and rule:** Adjacent angles on a straight line are supplementary, meaning their measures add up to $180^\circ$. So, $$ (x + 2) + 57 = 180 $$ 3. **Set up the equation:** $$ x + 2 + 57 = 180 $$ 4. **Simplify the left side:** $$ x + 59 = 180 $$ 5. **Isolate $x$ by subtracting 59 from both sides:** $$ x + \cancel{59} - \cancel{59} = 180 - 59 $$ $$ x = 121 $$ 6. **Answer:** The value of $x$ is $121$. This means the angle $(x + 2)^\circ$ is $123^\circ$ and together with $57^\circ$ they sum to $180^\circ$ as expected.