To find the missing angles $x$ and $y$, we will use a few key geometric principles:

1. Right Angle Property: The angle marked between the vertical and horizontal lines is a right angle, meaning it equals 90°.

2. Straight Angle Property: Angles on a straight line sum up to 180°.

Step-by-Step Solution:

• The given angle of $41^\circ$ and angle $x$ are on a straight line, meaning they are supplementary. Therefore, $x + 41^\circ = 180^\circ$ Solving for $x$: $x = 180^\circ - 41^\circ = 139^\circ$

• Next, angle $y$ is part of the right angle. Since the right angle sums to 90°, $41^\circ + y = 90^\circ$ Solving for $y$: $y = 90^\circ - 41^\circ = 49^\circ$

Final Answers:

• $x = 139^\circ$
• $y = 49^\circ$

Would you like further details on any of these steps?

Here are 5 related questions to practice with:

1. If the given angle was $35^\circ$, what would be the value of $x$ and $y$?
2. What is the sum of all angles around a point?
3. How would the solution change if the right angle was $100^\circ$ instead of $90^\circ$?
4. How can you find an unknown angle if you're given one angle of a right triangle?
5. What is the relationship between supplementary and complementary angles?

Tip: Always double-check whether the angles involved are forming a straight line (180°) or a right angle (90°).