1. **State the problem:** We need to find the measure of angle $\angle QWU$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the angles and relationships:** The lines are parallel, and the transversal creates corresponding angles. - Angle at $V$ is $(100 - 4x)^\circ$. - Angle at $W$ is $(106 - 7x)^\circ$. Since $V$ and $W$ lie on parallel lines cut by a transversal, these angles are corresponding angles and therefore equal: $$100 - 4x = 106 - 7x$$ 3. **Solve for $x$:** $$100 - 4x = 106 - 7x$$ $$-4x + 7x = 106 - 100$$ $$3x = 6$$ $$x = 2$$ 4. **Find $m\angle QWU$ by substituting $x=2$ into $(106 - 7x)^\circ$:** $$m\angle QWU = 106 - 7(2) = 106 - 14 = 92^\circ$$ 5. **Answer:** $$\boxed{92^\circ}$$ This is the measure of $\angle QWU$.