1. **State the problem:** We are given a triangle with three angles labeled as $ (8x - 4)^\circ $, $ (17x - 23)^\circ $, and $ (3x + 17)^\circ $. 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, $$ (8x - 4) + (17x - 23) + (3x + 17) = 180 $$ 3. **Combine like terms:** $$ 8x - 4 + 17x - 23 + 3x + 17 = 180 $$ $$ (8x + 17x + 3x) + (-4 - 23 + 17) = 180 $$ $$ 28x - 10 = 180 $$ 4. **Solve for $x$:** Add 10 to both sides: $$ 28x = 190 $$ Divide both sides by 28: $$ x = \frac{190}{28} = \frac{95}{14} $$ 5. **Final answer:** $$ x = \frac{95}{14} \approx 6.79 $$ This is the value of $x$ that satisfies the angle conditions of the triangle.