Question: Find the value of $a$ in rhombus EFGH.
Rhombus EFGH is in the center; angle at $E$ is labeled $a$ near the top-right, and angle at $G$ is labeled $2a-70^\circ$ near the bottom-left.
a = °
1. **State the problem:** We need to find the value of $a$ in rhombus $EFGH$ where angle $E = a$ and angle $G = 2a - 70^\circ$.
2. **Recall properties of a rhombus:** Opposite angles in a rhombus are equal, and adjacent angles are supplementary (sum to $180^\circ$).
3. **Set up the equation:** Since $E$ and $G$ are opposite angles, they are equal:
$$a = 2a - 70^\circ$$
4. **Solve for $a$:**
$$a = 2a - 70$$
$$a - 2a = -70$$
$$\cancel{a} - 2\cancel{a} = -70$$
$$-a = -70$$
$$a = 70^\circ$$
5. **Verify:** Adjacent angles $E$ and $F$ sum to $180^\circ$. Since $E = 70^\circ$, $F = 110^\circ$, which is consistent with rhombus properties.
**Final answer:**
$$a = 70^\circ$$