1. **State the problem:** We have a triangle with angles measuring $32^\circ$, $(7a + 4)^\circ$, and $(3(b + 2) - 1)^\circ$. We need to find the values of $a$ and $b$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is always $180^\circ$. So, $$32 + (7a + 4) + (3(b + 2) - 1) = 180$$ 3. **Simplify the expression:** $$32 + 7a + 4 + 3b + 6 - 1 = 180$$ $$32 + 4 + 6 - 1 + 7a + 3b = 180$$ $$41 + 7a + 3b = 180$$ 4. **Isolate the variables:** $$7a + 3b = 180 - 41$$ $$7a + 3b = 139$$ 5. **Interpretation:** We have one equation with two variables, so we need more information or assumptions to find unique values for $a$ and $b$. Since the problem does not provide more data, we can express one variable in terms of the other. 6. **Express $b$ in terms of $a$:** $$3b = 139 - 7a$$ $$b = \frac{139 - 7a}{3}$$ **Final answer:** The values of $a$ and $b$ satisfy the equation $$7a + 3b = 139$$. Without additional information, $b = \frac{139 - 7a}{3}$.