1. **State the problem:** We have four rays from the origin forming angles. One angle is 24° between the vertical right ray and an upward ray. We need to find the missing angles $x$ and $y$. 2. **Understand the setup:** The right horizontal ray is at 0°. - The upward ray is 24° from the vertical right ray. - The bottom vertical ray forms a right angle (90°) with the horizontal right ray. - The left ray is labeled $y$. - The angle $x$ is between the vertical right ray and the 24° ray. 3. **Use angle rules:** Angles around a point sum to 360°. 4. **Find $x$:** Since the 24° angle is between the vertical right ray and the upward ray, and $x$ is between the vertical right ray and the 24° ray, then $x = 24°$. 5. **Find $y$:** The left ray is opposite the right horizontal ray. The right horizontal ray is at 0°, so the left ray is at 180°. The angle $y$ is between the left ray (180°) and the vertical right ray (90°), so $$y = 180° - 90° = 90°$$ 6. **Final answers:** $$x = 24°$$ $$y = 90°$$