Question

use the figure to complete each part.
(a) name the vertex of \\( \angle dba \\).
(b) write two other names for \\( \angle cbd \\).
and
(c) name the sides of \\( \angle 1 \\).
and

Explanation:

Part (a)

Step 1: Recall vertex definition

The vertex of an angle is the common endpoint of its two sides. For $\angle DBA$, the sides are $\overrightarrow{BD}$ and $\overrightarrow{BA}$, so their common endpoint is $B$.

Part (b)

Step 1: Recall angle naming rules

An angle can be named by its vertex and two points (one on each side), or by its vertex alone if unique. For $\angle CBD$, sides are $\overrightarrow{BC}$ and $\overrightarrow{BD}$, so other names are $\angle DBC$ (reversing the side points) and $\angle 2$ (as labeled in the figure).

Part (c)

Step 1: Identify sides of $\angle 1$

$\angle 1$ has vertex $B$, with one side along $\overrightarrow{BC}$ and the other along $\overrightarrow{BA}$.

Answer:

(a) $B$
(b) $\angle DBC$, $\angle 2$
(c) $\overrightarrow{BC}$, $\overrightarrow{BA}$