1. **State the problem:** We have two intersecting lines forming four angles, with one angle given as 80° and its vertically opposite angle labeled as $y$. Below the intersecting lines, there is a triangle with one angle 50° and another angle labeled $x$. We need to find the values of $x$ and $y$. 2. **Use the property of vertically opposite angles:** Vertically opposite angles are equal. Therefore, $$y = 80^\circ$$ 3. **Use the triangle angle sum property:** The sum of angles in a triangle is always 180°. The triangle has angles $50^\circ$, $x$, and the third angle which is vertically opposite to $y$, so it is also $80^\circ$. 4. **Set up the equation:** $$50^\circ + x + 80^\circ = 180^\circ$$ 5. **Simplify and solve for $x$:** $$130^\circ + x = 180^\circ$$ $$x = 180^\circ - 130^\circ$$ $$x = 50^\circ$$ **Final answers:** $$x = 50^\circ, \quad y = 80^\circ$$