Angle G Parallelogram 4Ecdd6

1. **State the problem:** We need to find the measure of angle $G$ in parallelogram $EFGH$ given that $m\angle E = 2c + 9^\circ$ and $m\angle F = c$. 2. **Recall properties of parallelograms:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Use the supplementary angle rule:** Since $E$ and $F$ are adjacent angles, $$m\angle E + m\angle F = 180^\circ$$ Substitute the given expressions: $$2c + 9 + c = 180$$ 4. **Simplify and solve for $c$:** $$3c + 9 = 180$$ $$3c = 180 - 9$$ $$3c = 171$$ $$c = \frac{171}{3}$$ $$c = 57$$ 5. **Find $m\angle E$ and $m\angle F$:** $$m\angle E = 2c + 9 = 2(57) + 9 = 114 + 9 = 123^\circ$$ $$m\angle F = c = 57^\circ$$ 6. **Find $m\angle G$:** Opposite angles in a parallelogram are equal, so $$m\angle G = m\angle E = 123^\circ$$ **Final answer:** $$m\angle G = 123^\circ$$