In the diagram, we are dealing with two angles, $x$ and $y$, where the sum of the angles forms two sets of relationships:

1. $x$ and the given $41^\circ$ angle form a linear pair, meaning they are supplementary (add up to $180^\circ$).
2. $y$ and $41^\circ$ form a right angle (as indicated by the small square marking), meaning they add up to $90^\circ$.

Step-by-step solution:

1. For $x$:
   Since $x$ and $41^\circ$ are on a straight line, they are supplementary: $x + 41^\circ = 180^\circ$ Solving for $x$: $x = 180^\circ - 41^\circ = 139^\circ$

2. For $y$:
   The angle $y$ and $41^\circ$ are complementary, as they form a right angle: $y + 41^\circ = 90^\circ$ Solving for $y$: $y = 90^\circ - 41^\circ = 49^\circ$

Final answers:

• $x = 139^\circ$
• $y = 49^\circ$

Would you like more details on this, or have any other questions?

Here are 5 related questions:

1. What is the sum of all angles in a straight line?
2. What defines complementary and supplementary angles?
3. How do vertical angles behave in such problems?
4. What are alternate interior angles, and how do they relate to this type of diagram?
5. Can you calculate unknown angles when dealing with parallel lines cut by a transversal?

Tip: Remember, angles on a straight line always add up to 180°, while angles forming a right angle add up to 90°.