Question

which angle is formed by $overrightarrow{ed}$ and $overrightarrow{ef}$? select all that apply.
diagram with points a, b, e, g, d, f, c; angles labeled 2, 3; options: a) $\angle 2$, b) $\angle 3$, c) $\angle ged$, d) $\angle def$, e) $\angle bef$

Explanation:

To determine the angle formed by $\overrightarrow{ED}$ and $\overrightarrow{EF}$, we analyze the vertex and the rays forming the angle:

• The vertex of the angle formed by $\overrightarrow{ED}$ and $\overrightarrow{EF}$ is point $E$, with the two rays being $\overrightarrow{ED}$ and $\overrightarrow{EF}$.
• Option A: $\angle 2$ is formed by $\overrightarrow{EB}$ (or $\overrightarrow{EA}$) and $\overrightarrow{EG}$, so it is not formed by $\overrightarrow{ED}$ and $\overrightarrow{EF}$.
• Option B: $\angle 3$ has vertex $E$ and is formed by $\overrightarrow{ED}$ and $\overrightarrow{EF}$, so it is correct.
• Option C: $\angle GED$ is formed by $\overrightarrow{EG}$ and $\overrightarrow{ED}$, not $\overrightarrow{ED}$ and $\overrightarrow{EF}$.
• Option D: $\angle DEF$ has vertex $E$ and is formed by $\overrightarrow{ED}$ and $\overrightarrow{EF}$, so it is correct.
• Option E: $\angle BEF$ is formed by $\overrightarrow{EB}$ and $\overrightarrow{EF}$, not $\overrightarrow{ED}$ and $\overrightarrow{EF}$.

Answer:

B. $\angle 3$, D. $\angle DEF$