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This is a triangle problem involving an exterior angle. Here is how to solve it:

### Step 1: Understand the Relationship Between the Exterior Angle and Interior Angles
The key concept here is that 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 \(154^\circ\), and the two non-adjacent interior angles are \(x^\circ\) and \(90^\circ\) (since there is a right angle inside the triangle).

Thus, the relationship is:

\[
154^\circ = x^\circ + 90^\circ
\]

### Step 2: Solve for \(x\)
We can now solve for \(x\) by isolating it:

\[
x^\circ = 154^\circ - 90^\circ
\]
\[
x^\circ = 64^\circ
\]

### Conclusion
The value of \(x\) is \(64^\circ\).

Would you like more details or have any other questions?

Here are some related questions:
1. How do you calculate exterior angles in non-right triangles?
2. What is the sum of all angles in a triangle?
3. How can the exterior angle theorem be applied in obtuse triangles?
4. What would happen if the exterior angle was changed to 120°?
5. Can you derive the interior angles of a triangle given two exterior angles?

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

A side of the triangle below has been extended to form an exterior angle of 154°. Find the value of x.

Learn how to use the Exterior Angle Theorem to find the value of x in a right triangle where an exterior angle measures 154°. This problem demonstrates key concepts of triangle angle relationships and is suitable for students in Grades 8-10.

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