1. **State the problem:** We are given a triangle $\triangle STV$ with $UW$ as the midsegment parallel to side $ST$. The lengths are given as $ST = p - 64$ and $UW = p - 80$. We need to find the value of $p$. 2. **Recall the midsegment theorem:** The midsegment of a triangle is parallel to one side and its length is half the length of that side. Mathematically, $$ UW = \frac{1}{2} ST $$ 3. **Set up the equation using the given lengths:** $$ p - 80 = \frac{1}{2} (p - 64) $$ 4. **Solve for $p$:** Multiply both sides by 2 to eliminate the fraction: $$ 2(p - 80) = p - 64 $$ $$ 2p - 160 = p - 64 $$ Subtract $p$ from both sides: $$ 2p - p - 160 = -64 $$ $$ p - 160 = -64 $$ Add 160 to both sides: $$ p = -64 + 160 $$ $$ p = 96 $$ 5. **Conclusion:** The value of $p$ is $96$.