1. **State the problem:** We have two triangles, each with angles labeled. We want to find the measure of angle $z$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Analyze the first triangle $y$:** It has angles $85^\circ$, $40^\circ$, and $z$. 4. **Set up the equation for triangle $y$:** $$85^\circ + 40^\circ + z = 180^\circ$$ 5. **Calculate $z$:** $$z = 180^\circ - 85^\circ - 40^\circ$$ $$z = 180^\circ - 125^\circ$$ $$z = 55^\circ$$ 6. **Check the second triangle $r$ for consistency:** It has angles $85^\circ$, $55^\circ$, and $z$ (the unknown angle). Since the other two angles are $85^\circ$ and $55^\circ$, the third angle must be: $$z = 180^\circ - 85^\circ - 55^\circ = 40^\circ$$ 7. **Conclusion:** The measure of angle $z$ depends on which triangle we refer to. For triangle $y$, $z = 55^\circ$. For triangle $r$, $z = 40^\circ$. Since the question asks for the measure of $z$ and the options are 40°, 55°, or 85°, the correct answer is $55^\circ$ for triangle $y$ and $40^\circ$ for triangle $r$. Given the problem context, the measure of $z$ is $55^\circ$. **Final answer:** $z = 55^\circ$