1. **State the problem:** We have a triangle with three angles: one is 40°, the second is labeled as $11z$, and the third is labeled as $9z$. We need to find the value of $z$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. So, $$40 + 11z + 9z = 180$$ 3. **Combine like terms:** $$40 + 20z = 180$$ 4. **Isolate $z$:** Subtract 40 from both sides: $$20z = 180 - 40$$ $$20z = 140$$ Divide both sides by 20: $$z = \frac{140}{20} = 7$$ 5. **Final answer:** $$\boxed{7}$$ So, the value of $z$ is 7 degrees.