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The question in the image is asking about an isosceles triangle with two given angles, \( 70^\circ \) and \( x^\circ \), and is asking how many possible values of \( x \) can exist.

### Solution:

In an isosceles triangle, two of the angles are equal. There are two possible cases:

1. **Case 1**: The angle \( 70^\circ \) represents one of the two equal angles.
   - The sum of the angles in any triangle is always \( 180^\circ \).
   - Therefore, if the two equal angles are \( 70^\circ \), then the third angle is:
     \[
     180^\circ - 2(70^\circ) = 180^\circ - 140^\circ = 40^\circ
     \]
   - Thus, in this case, \( x = 40^\circ \).

2. **Case 2**: The angle \( 70^\circ \) represents the unequal angle.
   - In this case, the two equal angles are \( x^\circ \), and the sum of the angles is again \( 180^\circ \):
     \[
     70^\circ + 2x = 180^\circ
     \]
   - Solving for \( x \):
     \[
     2x = 180^\circ - 70^\circ = 110^\circ
     \]
     \[
     x = \frac{110^\circ}{2} = 55^\circ
     \]

### Conclusion:
There are two possible values for \( x \):
- \( x = 40^\circ \)
- \( x = 55^\circ \)

Would you like further details or clarification on any of these steps?

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Here are some related questions for you:

1. How do we calculate the sum of angles in any triangle?
2. What are the properties of an isosceles triangle?
3. Can the value of \( x \) be different if the triangle type changes?
4. What is the relationship between the angles and sides in an isosceles triangle?
5. How can you use this method for solving other types of triangles?

**Tip**: Always remember that the sum of the angles in any triangle must add up to \( 180^\circ \), which helps determine missing angle values easily.

Dua sudut segitiga sama kaki berukuran 70° dan x°. Berapakah jumlah ketiga nilai x yang mungkin?

Find the possible values of x in an isosceles triangle with two angles measuring 70° and x°. This problem covers the isosceles triangle theorem and the triangle angle sum theorem, suitable for students in Grades 8-10.

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