Question

use the figure to complete each part. (a) name the vertex of ∠hfe. ∠f (b) name the sides of ∠2. e f h→ and h f e→ (c) write two other names for ∠1. e f g→ and g f e→

Explanation:

Step1: Recall vertex - angle relationship

The vertex of an angle is the common endpoint of the rays that form the angle. For $\angle HFE$, the common endpoint of the rays $\overrightarrow{FH}$ and $\overrightarrow{FE}$ is point $F$.

Step2: Recall sides - angle relationship

The sides of an angle are the rays that form the angle. For $\angle 2$ (which is $\angle EFH$), the sides are $\overrightarrow{FE}$ and $\overrightarrow{FH}$.

Step3: Rename an angle

An angle can be named in different ways. For $\angle 1$ (which is $\angle EFG$), two other names are $\angle GFE$ and $\angle EFG$ (since the order of the points on the rays can be reversed when naming the angle with three - point notation as long as the vertex is in the middle).

Answer:

(a) $F$
(b) $\overrightarrow{FE}$ and $\overrightarrow{FH}$
(c) $\angle GFE$, $\angle EFG$