Question

Write a counterexample to show that the statement is false.

If two angles are supplementary, then they are a linear pair.
(a) Counterexample: Two right angles (90 degrees each)
(b) Counterexample: Two acute angles (less than 90 degrees each)
(c) Counterexample: Two obtuse angles (more than 90 degrees each)
(d) Counterexample: Two complementary angles (adding up to 90 degrees)

Answer 1

If two angles are supplementary, it does not necessarily mean they are a linear pair. A valid counterexample to the statement is two right angles.

Step-by-step explanation:

Suppose we have two angles that are supplementary, which means they add up to 180 degrees. In a linear pair of angles, the angles must be adjacent and form a straight line, which means they add up to 180 degrees. Therefore, if two angles are supplementary, it does not necessarily mean they are a linear pair.

For example, consider two right angles. Each right angle measures 90 degrees, so when you add them together, they still form a straight line and add up to 180 degrees. However, right angles are not adjacent angles, so they are not a linear pair.

Thus, a valid counterexample to the statement is two right angles.