Question

directions: select all that apply.
in the diagram below, what describes the relationship(s) between ∠1 and ∠2?
diagram of two parallel lines cut by a transversal, with angles labeled 1,2,3,4 on the top intersection and 5,6,7,8 on the bottom intersection
□ complementary angles
□ adjacent angles
□ supplementary angles
□ vertical angles

Explanation:

Step1: Recall Angle Relationship Definitions

• Complementary Angles: Sum to \(90^\circ\).
• Adjacent Angles: Share a common side and vertex, no overlapping interior.
• Supplementary Angles: Sum to \(180^\circ\).
• Vertical Angles: Opposite angles formed by intersecting lines, equal.

Step2: Analyze \(\angle 1\) and \(\angle 2\)

• Adjacent: \(\angle 1\) and \(\angle 2\) share a common vertex and side (the transversal), with non - overlapping interiors.
• Supplementary: They form a linear pair (on a straight line), so \(\angle 1+\angle 2 = 180^\circ\).
• Not Complementary: Their sum is \(180^\circ\), not \(90^\circ\).
• Not Vertical: Vertical angles are opposite (e.g., \(\angle 1\) and \(\angle 4\)), not adjacent.

Answer:

B. Adjacent Angles, C. Supplementary Angles