Question

select all of the angles for which $overrightarrow{ha}$ and $overrightarrow{he}$ are sides.
a) $angle1$
b) $angle6$
c) $angle ahe$
d) $angle age$
e) $angle eha$

Explanation:

Step1: Recall angle - naming convention

An angle is named using three points where the middle point is the vertex and the other two are on the rays (sides) of the angle. We are looking for angles with sides $\overrightarrow{HA}$ and $\overrightarrow{HE}$.

Step2: Check each option

• Option A: $\angle1$ has sides $\overrightarrow{GE}$ and $\overrightarrow{GF}$, not $\overrightarrow{HA}$ and $\overrightarrow{HE}$.
• Option B: $\angle6$ has sides $\overrightarrow{HB}$ and $\overrightarrow{HA}$, not $\overrightarrow{HA}$ and $\overrightarrow{HE}$.
• Option C: $\angle AHE$ has sides $\overrightarrow{HA}$ and $\overrightarrow{HE}$, so it is a correct option.
• Option D: $\angle AGE$ has sides $\overrightarrow{GA}$ and $\overrightarrow{GE}$, not $\overrightarrow{HA}$ and $\overrightarrow{HE}$.
• Option E: $\angle EHA$ has sides $\overrightarrow{HE}$ and $\overrightarrow{HA}$, so it is a correct option.

Answer:

C. $\angle AHE$, E. $\angle EHA$