1. **State the problem:** We are given that XZ bisects \(\angle WXY\). The measure of \(\angle WXY\) is \((4x + 2)^\circ\) and the measure of \(\angle WXZ\) is \((3x - 8)^\circ\). We need to find the measure of \(\angle WXZ\) in degrees. 2. **Recall the angle bisector property:** If XZ bisects \(\angle WXY\), then \(\angle WXZ = \angle ZXY = \frac{1}{2} \times \angle WXY\). 3. **Set up the equation:** $$ 3x - 8 = \frac{1}{2} (4x + 2) $$ 4. **Solve for \(x\):** $$ 3x - 8 = 2x + 1 $$ Subtract \(2x\) from both sides: $$ 3x - 2x - 8 = 1 $$ $$ x - 8 = 1 $$ Add 8 to both sides: $$ x = 9 $$ 5. **Find \(\angle WXZ\):** Substitute \(x = 9\) into \(3x - 8\): $$ 3(9) - 8 = 27 - 8 = 19 $$ 6. **Answer:** The measure of \(\angle WXZ\) is \(19^\circ\).