1. Problem: Given parallelogram LOVE with $LO = 16$, find $EV$. Step 1: Recall that in a parallelogram, opposite sides are equal in length. Step 2: Since $LO$ and $EV$ are opposite sides, $EV = LO$. Step 3: Therefore, $EV = 16$. 2. Problem: Given $m\angle E = 80^\circ$, find $m\angle V$. Step 1: In a parallelogram, consecutive angles are supplementary, meaning their measures add up to $180^\circ$. Step 2: Angles $E$ and $V$ are consecutive, so $m\angle E + m\angle V = 180^\circ$. Step 3: Substitute $m\angle E = 80^\circ$: $$80^\circ + m\angle V = 180^\circ$$ Step 4: Solve for $m\angle V$: $$m\angle V = 180^\circ - 80^\circ = 100^\circ$$ 3. Problem: Given $m\angle V = 95^\circ$, find $m\angle L$. Step 1: Opposite angles in a parallelogram are equal. Step 2: Angles $V$ and $L$ are opposite, so $m\angle L = m\angle V = 95^\circ$. 4. Problem: Given $EO = 20$, find $DE$. Step 1: The diagonals of a parallelogram bisect each other. Step 2: Point $D$ is the intersection of diagonals $LE$ and $OV$, so $D$ is the midpoint of $EO$. Step 3: Therefore, $DE = \frac{1}{2} EO = \frac{1}{2} \times 20 = 10$. 5. Problem: Given $DV = 9$, find $LV$. Step 1: Since $D$ is the midpoint of diagonal $OV$, $DV = DO = 9$. Step 2: The diagonal $OV$ length is $OV = DO + DV = 9 + 9 = 18$. Step 3: In a parallelogram, opposite sides are equal, but $LV$ is a side, not a diagonal. Step 4: However, $LV$ is opposite to $OE$, and since $LO$ and $EV$ are sides, $LV$ is equal to $OE$. Step 5: Without additional information about $LV$ or $OE$, we cannot determine $LV$ from $DV$ alone. Step 6: But if the problem implies $LV$ equals $OV$ (which is not standard), then $LV = 18$. Step 7: Otherwise, insufficient data to find $LV$. Final answers: 1. $EV = 16$ 2. $m\angle V = 100^\circ$ 3. $m\angle L = 95^\circ$ 4. $DE = 10$ 5. $LV$ cannot be determined with given data.