Question

How can complementary angles not be adjacent but share a common vertex?

Answer 1

See below for one solution.

Explanation:

There are several ways to do this. Here is one.

Draw a right triangle ABC with the right angle at C. Construct the line through C parallel to the hypoteneuse. This defines a pair of acute angles outside the triangle having common vertex C. These two angles are congruent to the A and B angles in the triangle and so are complementary, but they are not adjacent because the triangle's right angle intervenes.