The properties and characteristics of a triangle can be considered while solving this problem.
Given triangle ABC, we want to find a reflection that would carry this triangle onto itself.
Performing a 360-degree rotation (option b) on ABC would effectively change nothing because the triangle would end up where it started. It isn't a reflection.
A vertical reflection (option d) on triangle ABC would flip it upside down. This will not carry the triangle onto itself unless it is an isosceles triangle with an apex angle of 180 degrees, an impossible triangle to form.
As for option c, no reflection meant nothing changes or no action is taken on triangle ABC which doesn't satisfy the given question.
Therefore, the only plausible answer is a 180-degree rotation (option a). This rotation means flipping the triangle around its center, giving us the original triangle i.e., carrying the triangle onto itself. This is because the 180-degree rotation turns every point of a shape around a central point by half a circle, and the original triangle is resulted back. Hence, for the given triangle ABC, the set of reflections that carry it onto itself is a 180-degree rotation.