Question

use the figure to complete each part. (a) name the sides of ∠2. and (b) write two other names for ∠1. and (c) name the vertex of ∠dbc.

Explanation:

Step1: Identify sides of ∠2

A ray - based definition of an angle's sides is used. For ∠2, the sides are the rays that form it.
The sides of ∠2 are $\overrightarrow{BC}$ and $\overrightarrow{BD}$.

Step2: Find other names for ∠1

An angle can be named by the vertex alone (if there is no ambiguity) or by three - point naming. Since ∠1 has vertex B, two other names are ∠ABC and ∠CBA.

Step3: Determine vertex of ∠DBC

The vertex of an angle is the common endpoint of the rays that form the angle. For ∠DBC, the vertex is point B.

Answer:

(a) $\overrightarrow{BC}$ and $\overrightarrow{BD}$
(b) ∠ABC and ∠CBA
(c) B