1. **State the problem:** We need to find the value of $a$ in rhombus FGHI where angle $I = a + 56^\circ$ and angle $G = 8a$.\n\n2. **Recall properties of a rhombus:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$).\n\n3. **Set up the equation:** Since $I$ and $G$ are adjacent angles, we have:\n$$ (a + 56) + 8a = 180 $$\n\n4. **Simplify the equation:**\n$$ a + 56 + 8a = 180 $$\n$$ 9a + 56 = 180 $$\n\n5. **Isolate $a$:**\n$$ 9a = 180 - 56 $$\n$$ 9a = 124 $$\n\n6. **Solve for $a$:**\n$$ a = \frac{124}{9} $$\n\n7. **Show cancellation:**\n$$ a = \frac{\cancel{124}}{\cancel{9}} \text{ (no common factors to cancel)} $$\n\n8. **Final answer:**\n$$ a = \frac{124}{9} \approx 13.78^\circ $$\n\nThus, the value of $a$ is approximately $13.78^\circ$.