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To find the value of \( x \) in the given problem, we can use the properties of angles, specifically those related to vertical angles and the fact that the angles in a right angle must sum to 90°.

### Step-by-Step Solution:

1. **Identify the given angles:**
   - One angle is given as \( 41^\circ \).
   - Another angle is expressed as \( (11x - 23)^\circ \).
   - There is a right angle, which measures \( 90^\circ \).

2. **Recognize the relationships:**
   - The two angles labeled \( 41^\circ \) and \( (11x - 23)^\circ \) are supplementary because they are adjacent and together form the right angle. This means:
   \[
   41^\circ + (11x - 23)^\circ = 90^\circ
   \]

3. **Set up the equation:**
   \[
   41 + 11x - 23 = 90
   \]

4. **Simplify the equation:**
   \[
   11x + 18 = 90
   \]

5. **Solve for \( x \):**
   \[
   11x = 90 - 18
   \]
   \[
   11x = 72
   \]
   \[
   x = \frac{72}{11}
   \]
   \[
   x = 6.5454 \quad (\text{approximately})
   \]

So, the value of \( x \) is approximately **6.55**.

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

Here are 5 related questions you might find helpful:
1. How do you find supplementary angles if one angle is unknown?
2. What is the significance of vertical angles in geometry?
3. How can you solve for \( x \) when multiple angles are given in an equation?
4. What is the relationship between adjacent angles and their sum?
5. How do right angles influence the equations we set up for finding unknown variables?

**Tip:** Remember that angles on a straight line always add up to 180°, which can be very useful in solving various angle-related problems.

Find the value of X in the given geometric figure.

Learn how to solve for X in a geometric problem involving supplementary angles in a right angle. This problem covers key concepts in geometry and algebra, including the use of equations to solve for unknowns. Suitable for students in Grades 8-10.

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