Final answer:
A counter-example to the statement that two angles adding up to 180° form a linear pair is the case of vertical angles, which can sum to 180° without being a linear pair, or angles from separate triangles that add up to 180° but are not adjacent.
Step-by-step explanation:
A counter-example to Mr. Martin's statement: "If the measures of two angles add up to 180°, then they form a linear pair" could be two angles that are opposite angles when two lines cross (known as vertical angles). Vertical angles are equal to one another, and if one pair of opposite angles are both 90°, their sum is 180°. However, these angles are not adjacent and do not form a linear pair.
Another example involves angles from two separate triangles. If you have a triangle with one angle measuring 60° and another non-adjacent triangle with an angle measuring 120°, these two angles sum to 180° but clearly do not form a linear pair because they are part of separate figures and are not adjacent. This example is consistent with the fact that the sum of the angles in a triangle is always 180° and provides a clear counterexample to the statement.