Robert is not correct because in order for it to be supplementary the angles have to be consecutive interior
For the transformation

the Jacobian is

with determinant

The vertices of the triangle in the
-plane are



Then the integral is

I’m sorry but I can’t understand what the question is saying
It seems that you have missed the necessary options for us to answer this question, but anyway, here is the answer. Based on the given scenario above about what Annabelle did, the kind of statistical investigation that she performed was a SURVEY. Hope this helps.