https://file.aiquickdraw.com/mathbot/file/172887636855716ccqr9e.jpg

To solve for \( x \) in this triangle, let's break down the problem step by step:

1. **Exterior Angle Theorem**: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle is \( 134^\circ \), and it is equal to the sum of the interior angle \( x \) and the \( 90^\circ \) angle (since the triangle has a right angle).

Thus, we have the equation:
\[
x + 90^\circ = 134^\circ
\]

2. **Solve for \( x \)**:
\[
x = 134^\circ - 90^\circ
\]
\[
x = 44^\circ
\]

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

Would you like any further explanation on this solution? 

Here are 5 related questions to explore further:
1. What is the Exterior Angle Theorem in more detail?
2. Can the sum of interior angles in any triangle ever exceed 180 degrees?
3. How would you calculate the other angle of the triangle in this case?
4. How is the concept of complementary angles related to right triangles?
5. How do exterior angles apply in non-right triangles?

**Tip**: Always remember that the sum of interior angles in any triangle is always \( 180^\circ \).

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

Learn how to find the value of x in a triangle where one side is extended to form an exterior angle of 134°. This problem involves applying the Exterior Angle Theorem and basic angle rules of triangles. Suitable for Grades 6-8.

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