1. **State the problem:** We have a triangle with three interior angles: 38°, 76°, and 6c°. We need to find the value of $c$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. So, $$38 + 76 + 6c = 180$$ 3. **Combine the known angles:** $$114 + 6c = 180$$ 4. **Isolate the term with $c$:** $$6c = 180 - 114$$ $$6c = 66$$ 5. **Solve for $c$ by dividing both sides by 6:** $$c = \frac{66}{6}$$ $$c = 11$$ **Final answer:** $$\boxed{11}$$