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The problem in the image shows a triangle with one of its sides extended, creating an external angle of \(131^\circ\). Inside the triangle, one of the angles is given as \(54^\circ\), and the unknown angle \(x^\circ\) is the one adjacent to the external angle.

We can solve this by using the exterior angle theorem, which states that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

So, applying this theorem:

\[
131^\circ = 54^\circ + x
\]

To find \(x\):

\[
x = 131^\circ - 54^\circ
\]

\[
x = 77^\circ
\]

Thus, the value of \(x\) is \(77^\circ\).

Would you like further explanation on this or have any additional questions?

Here are five related questions for practice:
1. What is the exterior angle theorem, and how is it used in triangle problems?
2. Can the sum of interior angles in any triangle exceed \(180^\circ\)?
3. How can we find the third angle in a triangle if two angles are known?
4. If an exterior angle is \(150^\circ\) and one interior angle is \(60^\circ\), what is the other interior angle?
5. What would happen to the exterior angle if the internal angle adjacent to it decreases?

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

Find the value of x in a triangle with an extended side. One exterior angle is 131°, and one interior angle is 54°.

This problem focuses on finding the missing angle in a triangle with an extended side using the exterior angle theorem. The given exterior angle is 131°, and one of the interior angles is 54°. Learn step-by-step how to solve for the unknown angle x.

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