Question

drag and drop the descriptions in the box that
correctly classifies the angle pairs
you may use multiple responses in the boxes.
\\( \angle a o b \\) and \\( \angle b o c \\) \\( \angle a o c \\) and \\( \angle c o d \\)
adjacent complementary
supplementary vertical

Explanation:

Step1: Recall the definitions

• Adjacent angles: share a common vertex and a common side, and no common interior points.
• Complementary angles: sum to \(90^{\circ}\).
• Supplementary angles: sum to \(180^{\circ}\).
• Vertical angles: opposite angles formed by two intersecting lines.

Step2: Analyze \(\angle AOB\) and \(\angle BOC\)

• They share vertex \(O\) and side \(OB\), so they are adjacent.
• \(\angle AOB = 90^{\circ}\), and \(\angle AOB+\angle BOC=\angle AOC\). Since \(\angle AOC\) is not \(90^{\circ}\) (from the figure), they are not complementary.
• \(\angle AOB+\angle BOC

eq180^{\circ}\) (as \(\angle AOB = 90^{\circ}\) and \(\angle BOC\) is acute), so not supplementary.

• Not vertical (not opposite by two - line intersection).

Step3: Analyze \(\angle AOC\) and \(\angle COD\)

• They share vertex \(O\) and side \(OC\), so adjacent.
• \(\angle AOC+\angle COD=\angle AOD = 180^{\circ}\) (since \(AOD\) is a straight line), so supplementary.
• \(\angle AOC+\angle COD

eq90^{\circ}\), not complementary.

• Not vertical (not opposite by two - line intersection).

Answer:

\(\angle AOB\) and \(\angle BOC\): adjacent; \(\angle AOC\) and \(\angle COD\): adjacent, supplementary