1. **State the problem:** We have a triangle with interior angles labeled as $12a$, $4a$, and $36^\circ$. We need to find the value of $a$. 2. **Recall the rule for interior angles of a triangle:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Set up the equation:** $$12a + 4a + 36 = 180$$ 4. **Combine like terms:** $$16a + 36 = 180$$ 5. **Isolate $a$ by subtracting 36 from both sides:** $$16a + \cancel{36} - \cancel{36} = 180 - 36$$ $$16a = 144$$ 6. **Divide both sides by 16 to solve for $a$:** $$\frac{16a}{\cancel{16}} = \frac{144}{\cancel{16}}$$ $$a = 9$$ **Final answer:** $$a = 9^\circ$$