1. **State the problem:** We need to find the measures of the missing angles $x$ and $y$ given a diagram with several arrows and angles. 2. **Given information:** - One angle is $41^\circ$ between the diagonal top-right arrow and the vertical arrow pointing down. - There is a right angle ($90^\circ$) between the horizontal arrow pointing left and the vertical arrow pointing down. - Angles $x$ and $y$ are unknown. 3. **Analyze the angles around the point:** The arrows form angles around a point, so the sum of angles around that point is $360^\circ$. 4. **Identify known angles:** - The right angle is $90^\circ$. - The angle marked $41^\circ$ is given. 5. **Express $x$ and $y$ in terms of known angles:** - Since $x$ is the angle between the diagonal top-right arrow and the vertical arrow pointing down, and this is given as $41^\circ$, we have $x = 41^\circ$. 6. **Find $y$:** - The angle $y$ is between the diagonal top-left arrow and the horizontal arrow pointing left. - The right angle ($90^\circ$) is between the horizontal arrow pointing left and the vertical arrow pointing down. - The diagonal top-left arrow and the diagonal top-right arrow are symmetric around the vertical axis, so the angle between the diagonal top-left arrow and the vertical arrow pointing down is also $41^\circ$. - Therefore, $y$ is the difference between the right angle and $41^\circ$: $$y = 90^\circ - 41^\circ = 49^\circ$$ 7. **Final answers:** $$x = 41^\circ$$ $$y = 49^\circ$$