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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?

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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°).

Find the measure of the missing angles in the given geometric figure with a 41° angle and two unknown angles, x and y.

Solve the problem of finding missing angles x and y in a geometric figure where a 41° angle is given. Learn how to use the supplementary and complementary angle theorems to find the correct values of x and y. This problem is suitable for students in Grades 6-8.

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