Question

what is the name of the pair of angles ∠abd and ∠dbe that have a common vertex and share a common side? linear pair supplementary angles adjacent angles vertical angles

Explanation:

To determine the name of the pair of angles \(\angle ABD\) and \(\angle DBE\) with a common vertex (\(B\)) and a common side (\(BD\)):

• Linear pair: Angles that form a straight line (sum to \(180^\circ\)) and are adjacent. While these angles might be a linear pair, the key feature here is the common vertex and side, not just the straight line.
• Supplementary angles: Angles that sum to \(180^\circ\), but this is about their measure, not their position.
• Adjacent angles: Angles with a common vertex, a common side, and non - overlapping interiors. \(\angle ABD\) and \(\angle DBE\) share vertex \(B\), share side \(BD\), and their interiors do not overlap.
• Vertical angles: Angles opposite each other when two lines intersect, sharing a common vertex but no common side (except the vertex). These angles do not fit this description.

So, based on the definition of adjacent angles (common vertex, common side, non - overlapping interiors), the pair \(\angle ABD\) and \(\angle DBE\) are adjacent angles.

Answer:

adjacent angles