Question: Find $GJ$ in parallelogram $GHIJ$.
$J$
$2v-75$
$G$
$I$
$v-12$
$v-26$
$H$
$GJ = $
1. **State the problem:** We need to find the length of side $GJ$ in parallelogram $GHIJ$ given the expressions for the sides.
2. **Recall properties of parallelograms:** Opposite sides of a parallelogram are equal in length. Therefore, $GJ = HI$ and $GH = JI$.
3. **Identify given sides:**
- Side $JI = 2v - 75$
- Side $GH = v - 26$
- Side $IH = v - 12$
- Side $GJ = ?$
4. **Use the property of opposite sides:** Since $GJ$ is opposite to $HI$, we have:
$$GJ = HI = v - 12$$
5. **Check consistency with other sides:** Since $JI$ and $GH$ are opposite sides, they must be equal:
$$2v - 75 = v - 26$$
6. **Solve for $v$:**
$$2v - 75 = v - 26$$
$$2v - \cancel{75} = v - \cancel{26}$$
$$2v - v = -26 + 75$$
$$v = 49$$
7. **Find $GJ$ by substituting $v=49$ into $v - 12$:**
$$GJ = 49 - 12 = 37$$
**Final answer:**
$$\boxed{37}$$