1. **State the problem:** We are given a kite ABCD with sides labeled as expressions involving variables $v$ and $w$: - $AB = 10v - 13$ - $BC = 8w - 24$ - $CD = 5w$ - $AD = 7v - 1.6$ We need to find the measure of each kite side. 2. **Recall kite properties:** In a kite, two pairs of adjacent sides are equal: - $AB = AD$ - $BC = CD$ 3. **Set up equations using the kite side equalities:** $$10v - 13 = 7v - 1.6$$ $$8w - 24 = 5w$$ 4. **Solve for $v$:** $$10v - 13 = 7v - 1.6$$ $$10v - 7v = -1.6 + 13$$ $$3v = 11.4$$ $$v = \frac{11.4}{3} = 3.8$$ 5. **Solve for $w$:** $$8w - 24 = 5w$$ $$8w - 5w = 24$$ $$3w = 24$$ $$w = \frac{24}{3} = 8$$ 6. **Calculate each side length:** - $AB = 10v - 13 = 10(3.8) - 13 = 38 - 13 = 25$ - $AD = 7v - 1.6 = 7(3.8) - 1.6 = 26.6 - 1.6 = 25$ - $BC = 8w - 24 = 8(8) - 24 = 64 - 24 = 40$ - $CD = 5w = 5(8) = 40$ 7. **Conclusion:** The kite sides measure: - $AB = AD = 25$ - $BC = CD = 40$ These satisfy the kite property of two pairs of equal adjacent sides.