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To solve for the value of \(x\), we can use the concept of exterior angles in a triangle.

An exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle is given as \(154^\circ\).

The interior angles of the triangle are:
1. \(x^\circ\) (the angle we need to find),
2. \(90^\circ\) (since it's a right triangle).

According to the exterior angle theorem:
\[
154^\circ = x^\circ + 90^\circ
\]

Now, solving for \(x\):
\[
x^\circ = 154^\circ - 90^\circ = 64^\circ
\]

Thus, the value of \(x\) is \(64^\circ\).

Would you like further details on this? Here are some related questions to explore:

1. What is the exterior angle theorem?
2. How do you find an unknown angle in a triangle?
3. What is the sum of interior angles in a triangle?
4. How does the exterior angle relate to the interior angles of a triangle?
5. What types of triangles have right angles?

**Tip:** In any triangle, the sum of the interior angles is always \(180^\circ\).

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

Learn how to find the value of x in a right triangle where one side has been extended to form an exterior angle of 154°. This problem involves the Exterior Angle Theorem, a key geometry concept, and is suitable for students in Grades 7-9.

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