Question

(a) name the vertex of ∠hfg.
(b) write two other names for ∠efh.
(c) name the sides of ∠1.

Explanation:

Step1: Recall vertex - definition

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

Step2: Recall angle - naming rules

An angle can be named by its vertex (when there is no ambiguity), or by three points with the vertex in the middle. For $\angle EFH$, two other names are $\angle 2$ and $\angle HFE$ since the vertex is $F$ and the rays are $\overrightarrow{FE}$ and $\overrightarrow{FH}$.

Step3: Identify angle - sides

The sides of an angle are the two rays that form the angle. For $\angle 1$, the two rays are $\overrightarrow{FE}$ and $\overrightarrow{FG}$.

Answer:

(a) $F$
(b) $\angle 2$, $\angle HFE$
(c) $\overrightarrow{FE}$, $\overrightarrow{FG}$