1. **State the problem:** We have a triangle with three interior angles: 34°, 38°, and 4a°. We need to find the value of $a$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always 180°. This means: $$34 + 38 + 4a = 180$$ 3. **Set up the equation:** $$34 + 38 + 4a = 180$$ 4. **Simplify the known angles:** $$72 + 4a = 180$$ 5. **Isolate $4a$:** $$4a = 180 - 72$$ $$4a = 108$$ 6. **Solve for $a$:** $$a = \frac{108}{4} = 27$$ 7. **Final answer:** $$a = 27^\circ$$ This means the value of $a$ is 27 degrees.