In the image, we see a triangle with two angles given:

• One angle inside the triangle is marked as $63^\circ$.
• The angle adjacent to the triangle (exterior angle) is marked as $125^\circ$.
• One interior angle of the triangle is marked as $a^\circ$, which we need to find.

Using the exterior angle theorem, we know that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Thus, we can set up the following equation:

$125^\circ = a^\circ + 63^\circ$

Solving for $a^\circ$:

$a^\circ = 125^\circ - 63^\circ = 62^\circ$

Thus, $a^\circ = 62^\circ$.

Would you like further clarification or additional details on this?

Here are 5 related questions to expand your understanding:

1. How can you confirm the value of the third angle in this triangle?
2. What is the significance of the exterior angle theorem in geometry?
3. How would you find the side lengths if you knew more information about the triangle?
4. Can you apply the sum of angles in any polygon using similar methods?
5. How does this problem change if the exterior angle was different?

Tip: Remember, the exterior angle theorem is a powerful tool in triangle geometry, relating an exterior angle to the opposite interior angles!