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To solve for \(x\) in the given triangle, we will utilize the properties of angles, particularly in a triangle.

### Step-by-Step Solution:

1. **External Angle Theorem**: 
   In any triangle, an exterior angle is equal to the sum of the two opposite interior angles. 

   In the diagram:
   - The angle \(x\) is the interior angle at the top.
   - The exterior angle at the bottom right is given as \(z + 50\).
   - The angle on the bottom left is \(z - 50\).

   According to the **exterior angle theorem**, we have:
   \[
   x = (z + 50) + (z - 50)
   \]

2. Simplifying the expression:
   \[
   x = z + 50 + z - 50
   \]
   \[
   x = 2z
   \]

Thus, the value of \(x\) is \(2z\).

Let me know if you would like further details or explanations!

### Relative questions to expand your understanding:
1. What is the Exterior Angle Theorem and how does it apply to all triangles?
2. How would the equation change if the given angles were in different forms, such as algebraic expressions involving variables?
3. Can you solve for \(z\) if additional information is provided about the triangle's angle measures?
4. How would the solution differ if the triangle was not a simple planar triangle but involved trigonometric properties?
5. Can you identify other scenarios where the external angle theorem is used in geometry?

### Tip:
Always ensure that the sum of interior angles of a triangle is 180°, which can help verify your results when working with triangles.

In the figure given below, find the value of x in a triangle where the left angle is (z - 50) and the right exterior angle is (z + 50).

This page provides a solution for finding the value of x using the external angle theorem in a triangle. The problem involves the sum of angles and applies basic geometry concepts, suitable for students in Grades 8-10.

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