1. **State the problem:** We are given an equation involving angles: $ (3x - 5) + (7x + 5) = 180 $. We need to find the value of $x$. 2. **Formula and rules:** The sum of adjacent angles on a straight line is $180^\circ$. This is the linear pair postulate. 3. **Set up the equation:** $$ (3x - 5) + (7x + 5) = 180 $$ 4. **Simplify the left side:** $$ 3x - 5 + 7x + 5 = 180 $$ $$ (3x + 7x) + (-5 + 5) = 180 $$ $$ 10x + 0 = 180 $$ 5. **Solve for $x$:** $$ 10x = 180 $$ $$ x = \frac{\cancel{10}x}{\cancel{10}} = \frac{180}{10} $$ $$ x = 18 $$ 6. **Answer:** The value of $x$ is $18$.