Question

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

Explanation:

Adjacent angles are defined as two angles that share a common vertex and a common side, and their non - common sides are on opposite sides of the common side. For $\angle ABD$ and $\angle DBE$, they share the common vertex $B$ (or $O$ in the diagram) and the common side $BD$ (or $OD$). Their non - common sides are $BA$ and $BE$ respectively, which are on different sides of the common side $BD$. So, by the definition of adjacent angles, $\angle ABD$ and $\angle DBE$ are adjacent angles.

Answer:

Adjacent angles