1. **State the problem:** We are given two rectangles ABCD and WXYZ. For ABCD, angles and some measures are given, and for WXYZ, side WZ is expressed as $7x - 6$. We need to find the length of side WZ. 2. **Analyze rectangle ABCD:** In rectangle ABCD, diagonals intersect at E, and angles are given: $m\angle AEB = 16^\circ$, $m\angle DEA = 164^\circ$, $m\angle BAE = 10^\circ$, and $m\angle EDC = 16^\circ$. Since ABCD is a rectangle, all angles are $90^\circ$, and diagonals are equal and bisect each other. 3. **Analyze rectangle WXYZ:** WXYZ is a rectangle, so opposite sides are equal and all angles are $90^\circ$. Side WZ is given as $7x - 6$. 4. **Find $x$ using properties of rectangles:** Since WXYZ is a rectangle, side WZ must be a positive length. Without additional information about $x$, we cannot solve for $x$ directly from the given data. 5. **Conclusion:** The problem does not provide enough information to find $x$ or the length of WZ. More data or relationships are needed. **Final answer:** Cannot determine WZ with given information.