https://r2.erweima.ai/mathbot/image/1725474199302t90u2ndv.jpg

To solve the problem, let's first identify the key elements in the image:

1. **Angles**: 
   - \( m(\angle EAB) = 115^\circ \)
   - \( m(\angle EGD) = 45^\circ \)
   - \( m(\angle AEG) = x^\circ \)

2. **Question**: We need to determine the value of \( x \) (i.e., the angle \( m(\angle AEG) \)).

### Steps to Solve:

1. **Identify the relationship between the angles**:
   - Since \( \angle EAB = 115^\circ \), and it forms a linear pair with \( \angle BAEG \) (which is along the straight line from B through A to G), we can deduce that:
     \[
     \angle BAEG = 180^\circ - 115^\circ = 65^\circ
     \]

2. **Using Triangle Sum Theorem**:
   - In \( \triangle AEG \), the sum of the angles must equal \( 180^\circ \). So, we have:
     \[
     x + 45^\circ + 65^\circ = 180^\circ
     \]
   - Simplifying, we get:
     \[
     x + 110^\circ = 180^\circ
     \]
     \[
     x = 70^\circ
     \]

Thus, the value of \( x \) is \( 70^\circ \).

Would you like any further details or have any questions? Here are some related questions for practice:

1. How do linear pairs of angles work in different geometrical shapes?
2. What is the Triangle Sum Theorem, and where is it commonly applied?
3. How can you use angle relationships to solve for unknown angles in complex diagrams?
4. What are the properties of supplementary angles?
5. Can this problem be approached using a different method?

**Tip**: When working with angles, always check if they form a linear pair or if they are within a triangle, as these relationships often simplify the problem.

Yukarıdaki verilere göre x kaç derecedir?

Solve for the angle x in a triangle using the Triangle Sum Theorem and linear pair relationships. This problem involves key geometric concepts suitable for students in Grades 8-10.

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