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To solve for \( x \) in the triangle, we can use the fact that the sum of the interior angles of any triangle is always 180°.

The given angles are:
- 109°
- 31°
- \( x \)° (the unknown angle)

Using the equation for the sum of the angles:

\[
109^\circ + 31^\circ + x^\circ = 180^\circ
\]

Simplifying:

\[
140^\circ + x^\circ = 180^\circ
\]

\[
x^\circ = 180^\circ - 140^\circ = 40^\circ
\]

So, the value of \( x \) is \( 40^\circ \).

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How can we use this method to find angles in any triangle?
2. What if the triangle was an equilateral one? How would the angles differ?
3. How does the triangle's angle sum relate to polygons with more sides?
4. What are the properties of triangles with angles greater than 90° (obtuse triangles)?
5. How would we approach this if the triangle was inscribed in a circle?

**Tip**: Always remember the triangle angle sum rule — it works for all triangles regardless of shape or size.

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Learn how to solve for the unknown angle x in a triangle with given angles 31° and 109°. This problem demonstrates the use of the Triangle Angle Sum Theorem and is suitable for students in Grades 6-8.

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