Question 999526

by definition:
Complementary Angles are 2 angles the sum of whose measures is 90°

the counterexample to show that each conjecture is false  for if
 <A and <B are complementary angles then they share a common side:
the counterexample: adjacent angles (two angles are adjacent when they have a {{{common}}}{{{ side}}} and a common vertex (corner point) and don't overlap)

some more examples:

a counterexample is an exception to a proposed general rule or law

 for example, consider the proposition "all students are lazy"
because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false
 thus, any hard-working student is a counterexample to "all students are lazy"
 more precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement)

or

the sum of two integers is always positive: a counterexample =>{{{-4+3=-1}}}
the product of two mixed numbers is never a whole number:
a counterexample => ({{{1}}}{{{ 1/4}}})({{{2}}}{{{ 2/5}}})={{{3}}}

all four-sided figures are rectangles: a counterexample =>parallelogram with no {{{90}}} degree angles