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!