1. **Problem:** Given parallelogram ABCD with $m\angle D = x$ and $m\angle A = 3x + 4$, find $x$. 2. **Formula and rules:** In a parallelogram, opposite angles are congruent and consecutive angles are supplementary. Since $\angle D$ and $\angle A$ are consecutive, their measures add to 180 degrees: $$m\angle D + m\angle A = 180$$ 3. **Set up the equation:** $$x + (3x + 4) = 180$$ 4. **Simplify:** $$4x + 4 = 180$$ 5. **Subtract 4 from both sides:** $$4x + \cancel{4} - \cancel{4} = 180 - 4$$ $$4x = 176$$ 6. **Divide both sides by 4:** $$\frac{4x}{\cancel{4}} = \frac{176}{\cancel{4}}$$ $$x = 44$$ 7. **Answer:** The value of $x$ is 44. **Final answer:** C. 44