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The question asks which equation can be used to determine the measure of angle \( x^\circ \), based on the diagram provided.

### Analysis:
- The triangle in the figure has three angles: \( x^\circ \), \( y^\circ \), and a right angle (\( 90^\circ \)).
- Additionally, we have an exterior angle of \( 125^\circ \).

In any triangle:
\[
x + y + 90^\circ = 180^\circ
\]
Because it's a right triangle and the sum of all angles in a triangle must be \( 180^\circ \).

The exterior angle theorem tells us that:
\[
125^\circ = y + 90^\circ
\]
Thus:
\[
y = 125^\circ - 90^\circ = 35^\circ
\]
Now, using the equation for the triangle's angles:
\[
x + 35^\circ + 90^\circ = 180^\circ
\]
Solving this:
\[
x + 125^\circ = 180^\circ
\]

### Conclusion:
The correct equation is:
\[
125 + x = 180
\]
This corresponds to option **D** in the provided answer choices.

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Would you like any further clarification on this solution?

### Follow-up questions:
1. What is the exterior angle theorem, and how is it used in this problem?
2. How can you determine the measure of \( y^\circ \) from this triangle?
3. What is the significance of the sum of angles in a triangle being 180 degrees?
4. How would the solution change if the exterior angle were different?
5. Can you solve for \( x^\circ \) in terms of other angles if \( y \) is unknown?

**Tip**: When working with triangles, always remember that the sum of the interior angles will always be \( 180^\circ \), regardless of the triangle's type.

Which equation can be used to determine the measure of x?

Explore how to determine the measure of angle x in a triangle with a 125° exterior angle using the exterior angle theorem. Suitable for students in Grades 7-9.

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