Question

boom cards angle relationships select all that apply. ∠qba and ∠cbs are: complementary supplementary adjacent vertical linear pair congruent

Explanation:

Step1: Identify angle properties

First, note that $\angle ABL$ is a right angle ($90^\circ$), so $\angle QBA + \angle QBL = 90^\circ$. Also, lines $AQ$ and $CS$ are vertical, so $\angle QBA$ and $\angle CBS$ are vertical angles (opposite each other at vertex $B$), meaning they are congruent.

Step2: Analyze each option

• Complementary: Sum to $90^\circ$; these angles are not part of a right angle pair together, so no.
• Supplementary: Sum to $180^\circ$; vertical angles are congruent, not supplementary unless they are right angles, which they are not here, so no.
• Adjacent: Share a side and vertex; these angles only share vertex $B$, no common side, so no.
• Linear Pair: Form a straight line (sum to $180^\circ$ and adjacent); they do not, so no.
• Vertical: Opposite angles formed by intersecting lines; yes, $AQ$ and $CS$ intersect at $B$, so $\angle QBA$ and $\angle CBS$ are vertical.
• Congruent: Vertical angles are always congruent; yes, their measures are equal.

Answer:

• Vertical
• Congruent