Determine whether the conjencture is true or false. Give counter example is false.
Given: two angles are supplementary.
Conjecture: the angles form a linear pair.
http://www.mathsisfun.com/geometry/supplementary-angles.html
To determine the truth of the conjecture, we need to assess whether all pairs of supplementary angles form a linear pair.
First, let's clarify the definitions:
1. Supplementary angles: Two angles are supplementary if their sum is equal to 180 degrees.
2. Linear pair: Two adjacent angles that form a straight line, i.e., the sum of their measures is equal to 180 degrees.
To test the conjecture, we need to find at least one pair of angles that are supplementary but do not form a linear pair. Here's how we can do that:
Consider the angles of 70 degrees and 110 degrees. These angles are supplementary because 70 + 110 = 180. However, they do not form a linear pair since they are not adjacent or next to each other.
Therefore, we have found a counterexample to the conjecture. The counterexample shows that the conjecture, "If two angles are supplementary, then they form a linear pair," is false.