Classify the angle pair using all names that apply Vertical Adjacent Complementary Supplementary 1 2
The Correct Answer and Explanation is:
Correct Answer:
Vertical
Explanation:
To classify the relationship between angle 1 and angle 2, we must analyze their position relative to each other based on geometric definitions. Let’s examine each option:
1. Vertical Angles:
- Definition: Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. They are located opposite each other and share a common vertex. A key property of vertical angles is that they are always congruent (equal in measure).
- Application: In the given diagram, the two lines intersect to form four angles. Angle 1 and angle 2 are directly opposite each other at the point of intersection. They share a vertex but do not share any sides.
- Conclusion: This perfectly matches the definition of vertical angles. Therefore, the angle pair is Vertical.
2. Adjacent Angles:
- Definition: Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
- Application: Angle 1 and angle 2 share a common vertex, but they do not share a common side. The sides of angle 1 are opposite rays to the sides of angle 2.
- Conclusion: Since they do not share a common side, they are not adjacent angles.
3. Complementary Angles:
- Definition: Complementary angles are two angles whose measures add up to 90 degrees.
- Application: The diagram does not provide any specific angle measures. Visually, both angle 1 and angle 2 appear to be obtuse (greater than 90 degrees). The sum of two obtuse angles cannot be 90 degrees. Without information indicating the angles sum to 90 degrees, we cannot classify them as complementary.
- Conclusion: The angle pair is not complementary.
4. Supplementary Angles:
- Definition: Supplementary angles are two angles whose measures add up to 180 degrees. A common example is a linear pair (two adjacent angles whose non-common sides form a straight line).
- Application: Angle 1 and angle 2 are not adjacent, so they do not form a linear pair. As vertical angles, they are equal in measure. Their sum would only be 180 degrees if each angle was 90 degrees (i.e., if the lines were perpendicular). Since this is not specified, we cannot assume they are supplementary.
- Conclusion: The angle pair is not supplementary.
Based on this analysis, the only classification that applies to the relationship between angle 1 and angle 2 is Vertical.
