Question

use the figure to name the sides of ∠4.
figure with points a, b, c, d, e and angles labeled 1, 2, 3, 4
options:
o a) $overrightarrow{ac}$, $overrightarrow{ad}$
o b) $overrightarrow{ca}$, $overrightarrow{cb}$
o c) $overrightarrow{ca}$, $overrightarrow{cd}$
o d) $overrightarrow{ad}$, $overrightarrow{de}$

Explanation:

Step1: Recall angle side definition

An angle is formed by two rays (sides) with a common vertex. For $\angle 4$, find its vertex and the two rays forming it.

Step2: Identify vertex and rays

The vertex of $\angle 4$ is point $C$. The two rays (sides) are $\overrightarrow{CA}$ (from $C$ to $A$) and $\overrightarrow{CD}$ (from $C$ to $D$)? Wait, no, wait. Wait, looking at the figure: $\angle 4$ is at point $C$? Wait, no, the angle $\angle 4$: let's check the points. The angle $\angle 4$ has vertex at $C$? Wait, the options: option C is $\overrightarrow{CA}$, $\overrightarrow{CD}$? Wait, no, wait the angle $\angle 4$: the vertex is $C$? Wait, the sides of an angle with vertex $C$: the two rays forming $\angle 4$ are $\overrightarrow{CA}$ and $\overrightarrow{CD}$? Wait, no, let's re-examine. Wait, the angle $\angle 4$: the vertex is $C$, and the two sides are the rays from $C$: one is $\overrightarrow{CA}$ (going to $A$) and the other is $\overrightarrow{CD}$ (going to $D$)? Wait, no, the option C is $\overrightarrow{CA}$, $\overrightarrow{CD}$. Wait, let's check the options:

Option A: $\overrightarrow{AC}$, $\overrightarrow{AD}$ – vertex $A$, not $C$.

Option B: $\overrightarrow{CA}$, $\overrightarrow{CB}$ – $\overrightarrow{CB}$ is going to $B$, but $\angle 4$ is between $CA$ and $CD$? Wait, maybe I misread. Wait, the figure: points $B$, $C$, $D$ are colinear (horizontal line). Point $A$ is above $C$, point $D$ has other lines. $\angle 4$ is at $C$, between $CA$ (up to $A$) and $CD$ (right to $D$)? Wait, no, the angle $\angle 4$: the two sides are the rays with common vertex $C$. So the sides are $\overrightarrow{CA}$ (from $C$ to $A$) and $\overrightarrow{CD}$ (from $C$ to $D$)? Wait, option C is $\overrightarrow{CA}$, $\overrightarrow{CD}$. Wait, let's confirm:

An angle's sides are the two rays that form it, sharing the same vertex. For $\angle 4$, vertex is $C$. The two rays are $\overrightarrow{CA}$ (starting at $C$, going to $A$) and $\overrightarrow{CD}$ (starting at $C$, going to $D$). So the sides are $\overrightarrow{CA}$ and $\overrightarrow{CD}$, which is option C. Wait, but the original selected option was B, but maybe that's a mistake. Wait, let's recheck:

Wait, the angle $\angle 4$: looking at the figure, the angle at $C$ between $CB$ (left to $B$) and $CA$ (up to $A$)? No, $B$, $C$, $D$ are on a straight line, so $CB$ and $CD$ are opposite rays? Wait, no, $B---C---D$ is a straight line, so $\overrightarrow{CB}$ is left, $\overrightarrow{CD}$ is right. $\angle 4$ is at $C$, between $\overrightarrow{CA}$ (up) and $\overrightarrow{CD}$ (right)? Or between $\overrightarrow{CA}$ (up) and $\overrightarrow{CB}$ (left)? Wait, the angle number 4: in the figure, $\angle 4$ is at $C$, between $CA$ and $CD$? Wait, maybe the labels: $\angle 1$ is at $A$, $\angle 4$ at $C$, $\angle 3$ and $\angle 2$ at $D$. So $\angle 4$: vertex $C$, sides are $\overrightarrow{CA}$ (from $C$ to $A$) and $\overrightarrow{CD}$ (from $C$ to $D$)? Wait, no, $\overrightarrow{CD}$ is from $C$ to $D$, and $\overrightarrow{CA}$ is from $C$ to $A$. So the sides are $\overrightarrow{CA}$ and $\overrightarrow{CD}$, which is option C. Wait, but the original selection was B, maybe a mistake. Wait, let's check the options again:

Option A: $\overrightarrow{AC}$, $\overrightarrow{AD}$ – vertex $A$, so no.

Option B: $\overrightarrow{CA}$, $\overrightarrow{CB}$ – $\overrightarrow{CB}$ is left, $\overrightarrow{CA}$ is up. If $\angle 4$ is between $CA$ and $CB$, but $B$, $C$, $D$ are colinear, so $CB$ and $CD$ are straight line. So $\angle 4$ would be between $CA$ and $CD$? Wait, maybe the figure's angle 4 is between $CA$ and $CD$. So the correct sides are $\overrightarrow{CA}$ and $\overrightarrow{CD}$, which is option C. Wait, but maybe I made a mistake. Wait, let's recall: the sides of an angle are the two rays that form the angle, with the common vertex. So for $\angle 4$, vertex is $C$, so the two rays must start at $C$. So $\overrightarrow{CA}$ (starts at $C$, goes to $A$) and $\overrightarrow{CD}$ (starts at $C$, goes to $D$) – so option C.

Answer:

C. $\overrightarrow{CA}$, $\overrightarrow{CD}$