$\displaystyle \overrightarrow{OE}$ can be seen to be completely contained in $\displaystyle \overrightarrow{GE}$ - that is, $\displaystyle \overrightarrow{OE}\subseteq \overrightarrow{GE}$. The union of a set and its subset is the containing set, so the correct response is $\displaystyle \overrightarrow{GE}$.

The diagram below shows $\displaystyle \overrightarrow{NO}$ and $\displaystyle \overrightarrow{XO}$ in red and green, respectively:

The union of the two sets is the set of points in one or the other; this set is the entire line containing the two rays, which is $\displaystyle \overleftrightarrow{NX}$.

Below is the diagram with midpoint $\displaystyle M$ of $\displaystyle \overline{EO}$ added; also, $\displaystyle \overrightarrow{GM}$, the ray starting at $\displaystyle G$ and passing through $\displaystyle M$, is in green.

A ray is named after, in order, its endpoint and any other point on the ray.  $\displaystyle \overrightarrow{GM}$ has $\displaystyle G$ as an endpoint, and also includes the points $\displaystyle E$ and $\displaystyle O$, so there are two valid alternative names, $\displaystyle \overrightarrow{GE}$ and $\displaystyle \overrightarrow{GO}$, among the choices. The correct response is $\displaystyle \overrightarrow{GE}$.

Below is the diagram with the points $\displaystyle K,L,R$, and $\displaystyle S$, as described, shown in green. Also, $\displaystyle \overrightarrow{RS}$, the ray that has endpoint $\displaystyle R$ and passes through $\displaystyle S$, is marked in red.

The ray also passes through $\displaystyle E,K,L,$ and $\displaystyle O$, so $\displaystyle \overrightarrow{RE}$, $\displaystyle \overrightarrow{RK}$, $\displaystyle \overrightarrow{RL}$, and $\displaystyle \overrightarrow{RO}$—all four given names—are also valid names for the ray. 

Complementary angles have degree measures that total $\displaystyle 90 ^{\circ }$, so the measure of an angle complementary to a $\displaystyle 72 ^{\circ }$ angle would have measure $\displaystyle (90-72)^{\circ } = 18 ^{\circ }$.

Two angles are congruent if they have the same degree measure, so an angle will be congruent to a $\displaystyle 48 ^{\circ }$ angle if its measure is also $\displaystyle 48 ^{\circ }$.

Supplementary angles have degree measures that total $\displaystyle 180 ^{\circ }$, so the measure of an angle complementary to a $\displaystyle 66 ^{\circ }$ angle would have measure $\displaystyle \left ( 180- 66 \right )^{\circ } = 114^{\circ }$.

Supplementary angles have degree measures that total $\displaystyle 180^{\circ}$, so an angle supplementary to $\displaystyle 68^{\circ}$ would measure $\displaystyle 180^{\circ}-68^{\circ}=112^{\circ}$.

Congruent angles have degree measures that are equal, so an angle congruent to $\displaystyle 58^{\circ}$ is $\displaystyle 58^{\circ}$. 

Complementary angles have degree measures that total $\displaystyle 90^{\circ}$, so an angle complementary to $\displaystyle 42^{\circ}$ would measure $\displaystyle 90^{\circ}-42^{\circ}=48^{\circ}$.