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To solve for \( x \), let's use the following steps:

### Step 1: Use the property of exterior angles
In any triangle, the exterior angle is equal to the sum of the two non-adjacent interior angles.

Here, the exterior angle is \( 134^\circ \), and the two non-adjacent interior angles are \( x^\circ \) and \( 90^\circ \) (since the triangle is a right triangle).

### Step 2: Set up the equation
\[
x + 90^\circ = 134^\circ
\]

### Step 3: Solve for \( x \)
\[
x = 134^\circ - 90^\circ = 44^\circ
\]

Thus, the value of \( x \) is \( 44^\circ \).

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

Here are 5 related questions to consider:
1. How does the exterior angle theorem apply to all triangles?
2. What are the properties of right triangles?
3. How can we confirm that the sum of the interior angles of a triangle always equals \(180^\circ\)?
4. How would the problem change if the exterior angle was different?
5. Can we solve for the other interior angle if both the exterior angle and \( x \) were known?

**Tip**: In any triangle, always remember that the sum of interior angles is \( 180^\circ \), which can help verify the correctness of solutions.

A side of the triangle below has been extended to form an exterior angle of 134°. Find the value of x.

Explore how to solve a triangle problem involving an exterior angle of 134°. Using the exterior angle theorem, determine the value of x. This problem covers right-angle triangles, exterior angles, and step-by-step math concepts. Suitable for students in Grades 8-10.

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