Thank you for the question.
Although it is inconvenient, "Adjacent angles", "Vertical angles", "Alternate interior angles", "Supplementary angles", and "Corresponding angles" are all nontechnical phrases/labels/headings.
[These phrases would be technical if they were involved in computation. In the example you included (Thank you for doing so!), the phrases/labels are not involved in computation and so are not technical. It would be rare for any of those phrases/labels to be involved in computation.]