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In the image, you have a problem involving the **triangle exterior angle theorem**. This theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Here's the situation:

- The exterior angle is given as \(132^\circ\).
- One of the opposite interior angles is \(17^\circ\).
- The other opposite interior angle is labeled as \(x^\circ\).

According to the exterior angle theorem:
\[
\text{Exterior angle} = \text{Opposite interior angle 1} + \text{Opposite interior angle 2}
\]
Substitute the known values:
\[
132^\circ = 17^\circ + x^\circ
\]

Now, solve for \(x\):
\[
x = 132^\circ - 17^\circ = 115^\circ
\]

Therefore, \(x = 115^\circ\).

Would you like more details or have any further questions?

Here are some related questions:
1. What is the triangle sum theorem, and how does it relate to this problem?
2. Can the exterior angle theorem be used for non-triangular polygons?
3. How do you find the exterior angle of a triangle if all three interior angles are known?
4. What are some real-world applications of the exterior angle theorem?
5. What happens if the exterior angle is smaller than one of the opposite interior angles?

**Tip:** Always remember that the sum of the interior angles of a triangle is \(180^\circ\). This helps in cross-checking your calculations!

Find the value of x given a triangle with an exterior angle of 132°, one interior angle of 17°, and an unknown angle x.

Learn how to use the triangle exterior angle theorem to find the value of x in a triangle where the exterior angle is 132°, and one of the interior angles is 17°. A step-by-step solution is provided, suitable for students in Grades 8-10.

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