Question

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

Explanation:

Part (a)

Step1: Recall vertex definition

The vertex of an angle is the common endpoint of its two sides. For \( \angle 1 \), the sides meet at point \( F \).

Step1: Identify angle sides

For \( \angle GFE \), the sides are the rays forming the angle. The rays are \( \overrightarrow{FE} \) and \( \overrightarrow{FG} \) (or their segment/ray names as per the figure: \( FE \) and \( FG \), or \( \overrightarrow{EF} \) and \( \overrightarrow{GF} \) but typically we use the rays with the vertex in the middle). So the sides are \( \overrightarrow{FE} \) (or \( FE \)) and \( \overrightarrow{FG} \) (or \( FG \)).

Step1: Recall angle naming rules

An angle can be named by the vertex and a point on each side, or by the vertex alone (if unique) or by number. For \( \angle 2 \), the vertex is \( F \), and the sides have points \( H \) and \( E \). So other names are \( \angle HFE \) and \( \angle EFH \).

Answer:

\( F \)

Part (b)