1. The problem states that in a parallelogram, two adjacent interior angles are given as $(7a - 4)^\circ$ and $(4a + 47)^\circ$. 2. Important property: Adjacent angles in a parallelogram are supplementary, meaning their sum is $180^\circ$. 3. Set up the equation using this property: $$ (7a - 4) + (4a + 47) = 180 $$ 4. Combine like terms: $$ 7a - 4 + 4a + 47 = 180 $$ $$ (7a + 4a) + (-4 + 47) = 180 $$ $$ 11a + 43 = 180 $$ 5. Subtract 43 from both sides: $$ 11a + \cancel{43} - \cancel{43} = 180 - 43 $$ $$ 11a = 137 $$ 6. Divide both sides by 11 to solve for $a$: $$ \frac{11a}{\cancel{11}} = \frac{137}{\cancel{11}} $$ $$ a = \frac{137}{11} $$ 7. Simplify the fraction if possible. Since 137 and 11 have no common factors other than 1, the fraction is in simplest form. **Final answer:** $$ a = \frac{137}{11} $$