1. **State the problem:** We have four rays originating from a point forming angles around it. Given one angle is 33° and a right angle of 90°, we need to find the missing angles $x$ and $y$. 2. **Recall the rule:** The sum of angles around a point is always 360°. 3. **Identify known angles:** One angle is 33°, another is 90° (right angle), and the other two are $x$ and $y$. 4. **Set up the equation:** $$33 + 90 + x + y = 360$$ 5. **Simplify:** $$123 + x + y = 360$$ 6. **Express $x + y$:** $$x + y = 360 - 123 = 237$$ 7. **Use the given angle relationships:** The angle $x$ is adjacent to the 33° angle and together they form a straight line with the vertical upward ray, so they sum to 90° (since the vertical and horizontal rays form a right angle). Thus: $$x + 33 = 90$$ 8. **Solve for $x$:** $$x = 90 - 33 = 57$$ 9. **Find $y$ using $x + y = 237$:** $$y = 237 - x = 237 - 57 = 180$$ **Final answers:** $$x = 57^\circ$$ $$y = 180^\circ$$