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To solve this problem, we need to use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

### Step-by-Step Solution:

1. The exterior angle given is \( 132^\circ \).
2. The two non-adjacent interior angles to this exterior angle are \( 17^\circ \) and \( x^\circ \).
3. Using the exterior angle theorem, we know:
   \[
   \text{Exterior Angle} = \text{Sum of Opposite Interior Angles}
   \]
   Therefore:
   \[
   132^\circ = 17^\circ + x^\circ
   \]
4. To solve for \( x \), subtract \( 17^\circ \) from both sides:
   \[
   x = 132^\circ - 17^\circ = 115^\circ
   \]

So, the value of \( x \) is \( 115^\circ \).

Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. What is the sum of all interior angles of any triangle?
2. How does the exterior angle theorem apply to other polygons?
3. Can a triangle have more than one exterior angle?
4. What is the sum of the exterior angles of a polygon, and how is it calculated?
5. What happens to the exterior angles as the number of sides of a polygon increases?

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

A side of the triangle below has been extended to form an exterior angle of 132°. Find the value of x.

Learn how to solve for the interior angle of a triangle when given an exterior angle of 132°. This geometry problem uses the Exterior Angle Theorem to find the value of x. Suitable for Grades 6-8 students.

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