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In this problem, we are given a triangle with one of its sides extended, creating an exterior angle of 125°. We are also given that one of the interior angles is 25°, and we are tasked with finding the value of \( x \), which represents the other interior angle.

### Solution Approach:

The key concept here is that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. This is known as the **Exterior Angle Theorem**.

According to the theorem:

\[
\text{Exterior angle} = \text{Opposite interior angles' sum}
\]

In this case, the exterior angle is 125°, and the opposite interior angles are \( x \) and 25°. Therefore, we can write the equation:

\[
125^\circ = x^\circ + 25^\circ
\]

Now, solve for \( x \):

\[
x = 125^\circ - 25^\circ
\]

\[
x = 100^\circ
\]

Thus, the value of \( x \) is \( 100^\circ \).

Would you like more details or explanations on any part of this? 

Here are five related questions:
1. How does the Exterior Angle Theorem apply to all triangles?
2. Can exterior angles be used to find all interior angles of a triangle?
3. What is the sum of all interior angles in any triangle?
4. How can you calculate missing angles if only one exterior angle is provided?
5. How does the Exterior Angle Theorem differ from the Interior Angle Sum Theorem?

**Tip:** When solving for angles in triangles, always check if an exterior angle can help simplify the calculation!

A side of the triangle below has been extended to form an exterior angle of 125°. Find the value of x.

Learn how to find the value of an interior angle in a triangle where the exterior angle is given as 125° and one interior angle is 25°. This solution uses the Exterior Angle Theorem and is suitable for students in Grades 6-8.

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