Question

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

Explanation:

Part (a)

Step1: Recall the definition of an angle's sides

An angle is formed by two rays with a common endpoint. For \( \angle GFE\), the two rays (sides) are \( \overrightarrow{FG}\) and \( \overrightarrow{FE}\).

Part (b)

Step1: Use angle - naming conventions

One way to name an angle is by using three points (vertex in the middle). Another way is using the vertex (when there is no ambiguity). For \( \angle2\), since the vertex is \(F\), and using three - point notation, we can write \( \angle MFE\) (because the angle is formed at \(F\) with rays \(FM\) and \(FE\)). Also, since the vertex is \(F\) and there is no ambiguity (as we are referring to the specific angle marked as \(2\)), we can write \( \angle F\) (in the context of the given figure where \(F\) is the vertex of the angle marked \(2\)).

Part (c)

Step1: Recall the definition of an angle's vertex

The vertex of an angle is the common endpoint of the two rays that form the angle. For \( \angle1\), the two rays are \( \overrightarrow{FG}\) and \( \overrightarrow{FE}\), and their common endpoint is \(F\).

Answer:

(a) \(\overrightarrow{FG}\) and \(\overrightarrow{FE}\)
(b) \(\angle MFE\) and \(\angle F\)
(c) \(F\)