1. **Problem Statement:** We need to find the measure of angle $\angle QWU$ given two angles formed by a transversal crossing two parallel lines: one angle at point $V$ is $(100 - 4x)^\circ$ and another at point $W$ is $(106 - 7x)^\circ$. 2. **Key Concept:** When a transversal crosses two parallel lines, corresponding angles are equal. Here, angles at $V$ and $W$ are corresponding angles, so: $$100 - 4x = 106 - 7x$$ 3. **Solve for $x$:** $$100 - 4x = 106 - 7x$$ Add $7x$ to both sides: $$100 + 3x = 106$$ Subtract 100 from both sides: $$3x = 6$$ Divide both sides by 3: $$x = 2$$ 4. **Find $m\angle QWU$:** The angle at $W$ is given by: $$(106 - 7x)^\circ = 106 - 7(2) = 106 - 14 = 92^\circ$$ 5. **Answer:** $$m\angle QWU = 92^\circ$$ This means the measure of angle $\angle QWU$ is $92^\circ$.