The question shows a triangle with an exterior angle labeled ∠A. The interior angles are labeled 60°, 80°, and 40°. The goal is to determine which statement about the exterior angle is correct.

Explanation:

For any triangle:

• The sum of the interior angles is always 180°.
• An exterior angle is equal to the sum of the two non-adjacent interior angles.

Here, the exterior angle ∠A is adjacent to the 40° interior angle, and the two non-adjacent interior angles are 60° and 80°.

Thus, the exterior angle ∠A should be:

$\text{Exterior Angle} = 60^\circ + 80^\circ = 140^\circ$

The correct answer should be:

"It is 140° because it is supplementary to 40°."

This means the selected answer, "It is 120° because 40° + 80° = 120°," is incorrect, as the rule of exterior angles involves adding the two non-adjacent angles (60° and 80°), not just one.

Would you like more details or have any other questions?

Here are 5 related questions to think about:

1. How do you determine the exterior angle in different types of triangles?
2. What is the sum of the interior angles in any polygon?
3. Why are the interior and exterior angles supplementary?
4. How would this concept change if the triangle were not right-angled?
5. Can you prove why the sum of the interior angles is always 180° for a triangle?

Tip: Always remember that an exterior angle is formed by extending one side of a triangle, and it equals the sum of the two opposite interior angles.