1. **Problem statement:** Given that SU is a midsegment of triangle $\triangle RTV$, and $RV = p$, $SU = p - 15$, 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. 3. **Apply the theorem:** Since SU is a midsegment parallel to RV, we have: $$SU = \frac{1}{2} RV$$ 4. **Substitute the given values:** $$p - 15 = \frac{1}{2} p$$ 5. **Solve for $p$:** Multiply both sides by 2 to clear the fraction: $$2(p - 15) = p$$ Simplify the left side: $$2p - 30 = p$$ Subtract $p$ from both sides: $$2p - p - 30 = 0 \implies p - 30 = 0$$ Add 30 to both sides: $$p = 30$$ 6. **Answer:** The value of $p$ is $30$.