Question

question name the marked angle in 2 different ways. watch video show examples answer attempt 1 out of 2 submit answer

Explanation:

Step1: Identify the vertex and rays

The angle has vertex \( G \), with one ray along \( GF \) and the other along \( GE \), or also considering the other ray \( GH \)? Wait, no, the marked angle is between \( GF \) and \( GE \)? Wait, looking at the diagram, the vertex is \( G \), and the two sides are \( GF \) (left) and \( GE \) (upper left), or maybe \( GF \) and \( GH \)? Wait, the marked angle is the purple one at \( G \), between \( GF \) (horizontal left) and \( GE \) (the other side). Wait, no, let's see: the points are \( F \), \( G \), \( E \), \( H \). So the angle can be named by the vertex and the two points, or by the vertex alone if unique.

Step2: Name using three points

First way: Using three points, with the vertex in the middle. So \( \angle FGE \) (since the sides are \( GF \) and \( GE \), vertex \( G \)).

Second way: Using the vertex alone, if there's only one angle at \( G \) (but here maybe also \( \angle EGF \) which is the same as \( \angle FGE \), or maybe \( \angle G \) if it's the only angle at \( G \), but usually with three points. Wait, maybe the other side is \( GH \)? Wait, no, the marked angle is between \( GF \) and \( GE \)? Wait, the diagram shows \( F \) to \( G \) (left), \( G \) to \( E \) (upper left), and \( G \) to \( H \) (upper right). The purple angle is between \( GF \) and \( GE \)? Wait, no, maybe between \( GF \) and \( GH \)? Wait, the user's diagram: let's re-express. The vertex is \( G \), with three rays: \( GF \) (left, horizontal), \( GE \) (upper left, slanting), \( GH \) (upper right, slanting). The marked angle (purple) is between \( GF \) and \( GE \)? Or between \( GF \) and \( GH \)? Wait, the problem says "marked angle", so looking at the diagram, the purple angle is between \( GF \) (left) and \( GE \) (the middle upper ray), or \( GF \) and \( GH \)? Wait, maybe I misread. Let's assume the marked angle is at \( G \), between \( F \) and \( E \), so vertex \( G \), sides \( GF \) and \( GE \).

So first way: \( \angle FGE \) (three-point notation, vertex in middle). Second way: \( \angle EGF \) (same angle, reversed order of points), or \( \angle G \) (if it's the only angle at \( G \), but usually with three points. Wait, maybe the other side is \( GH \), but the marked angle is between \( GF \) and \( GE \). Alternatively, maybe the angle is \( \angle FGE \) and \( \angle EGF \), or \( \angle G \) and \( \angle FGE \).

Wait, standard angle naming: using three points (vertex in middle) or using the vertex (if only one angle at that vertex). So for the angle at \( G \) between \( F \) and \( E \), we can name it \( \angle FGE \) (three points) and \( \angle G \) (vertex).

Answer:

\( \angle FGE \) and \( \angle G \) (or \( \angle EGF \) and \( \angle FGE \))