Question

which angle is formed by $overrightarrow{ea}$ and $overrightarrow{eg}$? select three that apply
diagram: points a, b, 2, e (vertex), g, d, c, f with rays; options: a) $angle 2$, b) $angle aeg$, c) $angle gae$ (checkboxes)

Explanation:

1. For angle formed by $\overrightarrow{EA}$ and $\overrightarrow{EG}$:

• $\angle 2$: The angle at vertex $E$ between $\overrightarrow{EA}$ (which is along the line $A - B - E$) and $\overrightarrow{EG}$ is labeled as $\angle 2$, so this is correct.
• $\angle AEG$: When we name an angle with three points, the middle point is the vertex. Here, vertex $E$ is between $A$ and $G$, so $\angle AEG$ is the angle formed by $\overrightarrow{EA}$ and $\overrightarrow{EG}$, this is correct.
• $\angle GAE$: In $\angle GAE$, the vertex is $A$, and the angle is formed by $\overrightarrow{AG}$ and $\overrightarrow{AE}$, not $\overrightarrow{EA}$ and $\overrightarrow{EG}$, so this is incorrect. Wait, maybe there are more options (the original problem says select three, but the given options here seem incomplete, but based on the visible options: $\angle 2$, $\angle AEG$ are correct, and if we assume there are other correct ones, but from the given visible options, let's re - check. Wait, the angle formed by $\overrightarrow{EA}$ (ray from $E$ to $A$) and $\overrightarrow{EG}$ (ray from $E$ to $G$) has vertex $E$. So $\angle 2$ (which is $\angle AEG$ with a number label) and $\angle AEG$ are the same angle. Also, if we consider the notation, $\angle GAE$ has vertex $A$, so it's wrong. But maybe in the original problem, there are more options. But based on the given visible options, the correct ones among the shown are $\angle 2$ (A) and $\angle AEG$ (B). But since the problem says select three, maybe there are other options not fully shown. But from the given:
• $\angle 2$: Correct, as it's the angle between $\overrightarrow{EA}$ and $\overrightarrow{EG}$ at $E$.
• $\angle AEG$: Correct, as the angle with vertex $E$, sides $EA$ and $EG$.
• (Assuming there is a third correct option, but from the given, maybe a typo or missing options. But based on the shown, A and B are correct. Wait, maybe the third one is $\angle GEA$ (same as $\angle AEG$), but in the given options, A, B are correct. But the problem says select three, so maybe there are more options not visible. But based on the current information, the correct options among the shown are:

Answer:

A) $\angle 2$, B) $\angle AEG$ (and a third correct option which is not fully visible in the provided image, but from the given choices, these two are correct. If we assume a third, maybe a similar - named angle with vertex $E$ for the two rays $\overrightarrow{EA}$ and $\overrightarrow{EG}$)