Question

use the figure to complete each part.
(a) write two other names for ∠cbd.
and
(b) name the vertex of ∠dba.

(c) name the sides of ∠1.
and

Explanation:

Part (a)

Step1: Recall angle naming rules

An angle can be named by the vertex and two points (one on each side), with the vertex in the middle, or by the number if labeled, or by the vertex alone if unique. For $\angle CBD$, the vertex is $B$, sides are $BC$ and $BD$. So other names can be $\angle DBC$ (reversing the side points with vertex in middle) and $\angle 2$ (since it's labeled as $\angle 2$).

Step2: Confirm the names

• $\angle DBC$: vertex $B$, sides $BD$ and $BC$ (order reversed from $\angle CBD$).
• $\angle 2$: the angle is labeled as $\angle 2$, so it can be named $\angle 2$.

Step1: Recall vertex definition

The vertex of an angle is the common endpoint of the two rays forming the angle. For $\angle DBA$, the rays are $BD$ and $BA$, with common endpoint $B$.

Step1: Identify $\angle 1$

$\angle 1$ is formed by rays $BA$ and $BC$ with vertex $B$.

Step2: Name the sides

The sides of $\angle 1$ are the two rays forming it, which are $\overrightarrow{BA}$ and $\overrightarrow{BC}$ (or just the segments $BA$ and $BC$ as the sides of the angle).

Answer:

(a):
$\boldsymbol{\angle DBC}$ and $\boldsymbol{\angle 2}$

Part (b)