Question

which angle is formed by \\( \overrightarrow{ea} \\) and \\( \overrightarrow{eg} \\)? select all that apply.
a) \\( \angle 2 \\)
b) \\( \angle 3 \\)
c) \\( \angle geb \\)
d) \\( \angle gae \\)
e) \\( \angle aeg \\)

Explanation:

Step1: Recall the definition of an angle

An angle is formed by two rays with a common endpoint. Here, the rays are \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\), and the common endpoint is \(E\).

Step2: Analyze each option

• Option A (\(\angle2\)): \(\angle2\) is the angle between \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\) as per the diagram's labeling.
• Option B (\(\angle3\)): \(\angle3\) is between different rays (\(\overrightarrow{ED}\) or \(\overrightarrow{EF}\) and another ray, not \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\)).
• Option C (\(\angle GEB\)): The vertex of \(\angle GEB\) is \(E\), but the sides are \(\overrightarrow{EG}\) and \(\overrightarrow{EB}\) (not \(\overrightarrow{EA}\)). Since \(\overrightarrow{EA}\) and \(\overrightarrow{EB}\) are collinear (same - line rays), \(\angle GEB\) is not the angle formed by \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\).
• Option D (\(\angle GAE\)): The vertex of \(\angle GAE\) is \(A\), but the common endpoint of \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\) is \(E\).
• Option E (\(\angle AEG\)): By the angle - naming convention (vertex in the middle), \(\angle AEG\) has vertex \(E\) and sides \(\overrightarrow{EA}\) and \(\overrightarrow{EG}\).

Answer:

A. \(\angle2\), E. \(\angle AEG\)