https://file.aiquickdraw.com/mathbot/file/1726770481485cfucd30n.jpg

To solve for \( x \) in this diagram, let's analyze the given angles and apply angle relationships.

### Step-by-step solution:

1. **Triangle Angle Sum**: In the triangle, you are given two angles:
   - \( 47^\circ \)
   - \( 41^\circ \)
   The sum of the interior angles of a triangle is always \( 180^\circ \). Thus, the third angle \( y \) in the triangle is:
   \[
   y = 180^\circ - (47^\circ + 41^\circ) = 180^\circ - 88^\circ = 92^\circ
   \]

2. **Linear Pair**: Angle \( y \) forms a linear pair with \( x \), meaning they are supplementary (their sum is \( 180^\circ \)):
   \[
   x = 180^\circ - 92^\circ = 88^\circ
   \]

Thus, \( x = 88^\circ \).

### Correct answer: \( 88^\circ \).

Let me know if you need more details, or have any questions!

Here are 5 related questions you can explore:
1. What are the properties of supplementary angles?
2. Can you solve for the third angle in any triangle?
3. How do linear pairs work in more complex geometric figures?
4. How can the angle sum property help in real-life triangle applications?
5. How would this change if the given angles were obtuse?

**Tip**: In any triangle, the exterior angle is always equal to the sum of the two opposite interior angles!

Find the value of x given two angles in a triangle (47° and 41°) and angle y adjacent to angle x, forming a linear pair.

This problem involves solving for x in a geometric figure using the triangle angle sum property and the linear pair theorem. Given two angles in a triangle (47° and 41°), find the third angle and solve for x. Suitable for students in Grades 7-9.

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