To determine which pair of angles acts as a counterexample to the statement "A pair of supplementary angles are adjacent to each other," we first need to understand what supplementary angles and adjacent angles are.
1. Supplementary Angles: Two angles are supplementary if their measures add up to 180 degrees.
2. Adjacent Angles: Two angles are adjacent if they share a common side and a common vertex (corner point) and do not overlap.
The given statement claims that all pairs of supplementary angles are adjacent. To find a counterexample, we need to find a pair of supplementary angles that are not adjacent to each other.
Let's examine the given angle pairs:
1. 60° and 120°:
- Sum = 60° + 120° = 180°
- Since their sum is 180°, they are supplementary.
- They are not necessarily adjacent because they do not have to share a common side or vertex.
2. 90° and 90°:
- Sum = 90° + 90° = 180°
- Although they are supplementary, they can be adjacent if they share a common side and vertex (like two right angles forming a straight line). However, this pair can also be non-adjacent.
3. There is no counterexample: This option suggests that the other pairs do not provide a counterexample, which we need to verify.
4. 40° and 140°:
- Sum = 40° + 140° = 180°
- Their sum is 180°, making them supplementary. Like the pair of 60° and 120°, they are not necessarily adjacent.
Among the provided pairs, we notice that both (60°, 120°) and (40°, 140°) are valid examples of supplementary angles. However, they do not have to be adjacent to be supplementary.
Thus, the pair 60° and 120° serves as a clear counterexample to the statement "A pair of supplementary angles are adjacent to each other."
