For each interior angle at the vertex of a triangle, there are two possible exterior angles. Is this statement true or false?

This statement is true.

To understand why, let's consider the definitions and properties of angles in a triangle:

1. Interior Angles: In any triangle, the three angles inside the triangle are known as interior angles.

2. Exterior Angles: An exterior angle is formed when a side of the triangle is extended. Each interior angle has a corresponding exterior angle adjacent to it.

3. Exterior Angles Correspondence: For each interior angle at a vertex of a triangle, you can extend either side of the triangle connected to that vertex, leading to two distinct exterior angles for that interior angle.

Thus, for each of the triangle's three interior angles, there are indeed two possible exterior angles based on the side chosen for extension, confirming that the statement is true.