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To solve this problem, we can use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Here, we are given:
- An exterior angle of \( 64^\circ \).
- One interior angle \( 49^\circ \).

Let the unknown angle \( x \) be the other interior angle of the triangle.

According to the exterior angle theorem:
\[
\text{Exterior angle} = \text{Sum of the two opposite interior angles}
\]
Thus,
\[
64^\circ = x + 49^\circ
\]
Now, solving for \( x \):
\[
x = 64^\circ - 49^\circ = 15^\circ
\]

So, the value of \( x \) is \( 15^\circ \).

Do you need any further explanation or details?

Here are 5 related questions:
1. How is the exterior angle theorem derived from the triangle angle sum property?
2. Can the exterior angle of a triangle ever be smaller than any of its interior angles?
3. How do you determine the third interior angle of a triangle if two interior angles are known?
4. How does the exterior angle relate to the interior angle adjacent to it?
5. How can this concept be applied to non-triangular polygons?

**Tip**: Remember, the exterior angle theorem is a quick way to find unknown angles in a triangle when the exterior angle and one of the opposite angles are known!

A side of the triangle below has been extended to form an exterior angle of 64°. Find the value of x.

Learn how to solve for the value of x in a triangle problem where a side has been extended to form an exterior angle of 64°. This problem involves the use of the exterior angle theorem and covers key geometry concepts. Suitable for students in Grades 7-9.

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