1. **State the problem:** We have a rhombus W T U V with diagonals intersecting at point X. Given UV = 8 and WX = 5, find the missing measures. 2. **Recall properties of a rhombus:** All sides are equal in length. 3. **Diagonals in a rhombus:** They bisect each other at right angles. 4. **Given:** UV = 8, WX = 5, TU = 8, WU = 10, TX = 6.2, TV = 12.5. 5. **Check side lengths:** Since rhombus sides are equal, TU = UV = WU = TV = 8. But WU = 10 and TV = 12.5 contradict this, so these must be other segments, not sides. 6. **Diagonals bisect each other:** X is midpoint of both diagonals. 7. **Calculate half diagonals:** $$ UX = \frac{UV}{2} = \frac{8}{2} = 4 $$ $$ WX = 5 \text{ (given)} $$ 8. **Use Pythagoras theorem in triangle W X U:** $$ WU^2 = WX^2 + UX^2 $$ $$ WU^2 = 5^2 + 4^2 = 25 + 16 = 41 $$ $$ WU = \sqrt{41} \approx 6.4 $$ 9. **Check given WU = 10:** This contradicts the rhombus property; likely a mislabel or different segment. 10. **Similarly, check triangle T X V:** $$ TV^2 = TX^2 + XV^2 $$ Since UV = 8, XV = UX = 4. $$ TV^2 = 6.2^2 + 4^2 = 38.44 + 16 = 54.44 $$ $$ TV = \sqrt{54.44} \approx 7.38 $$ 11. **Given TV = 12.5 contradicts this; likely a mislabel or different segment.** 12. **Conclusion:** The sides of the rhombus are all equal to approximately 6.4 (from step 8). **Final answer:** The side length of the rhombus is approximately $6.4$ units.