Question

use the figure to name the sides of ∠4.
a) $overrightarrow{ac}$, $overrightarrow{ad}$
b) $overrightarrow{ca}$, $overrightarrow{cb}$
c) $overrightarrow{ca}$, $overrightarrow{cd}$

Explanation:

To determine the sides of \(\angle 4\), we first identify the vertex of \(\angle 4\), which is point \(C\). The sides of an angle are the two rays that form the angle, both starting from the vertex. For \(\angle 4\) at vertex \(C\), we look at the rays originating from \(C\). The rays are \(\overrightarrow{CA}\) (from \(C\) to \(A\)) and \(\overrightarrow{CB}\) (from \(C\) to \(B\)). Let's check the options:

• Option A: \(\overrightarrow{AC}\) starts at \(A\), not \(C\) (vertex of \(\angle 4\)), so incorrect.
• Option B: \(\overrightarrow{CA}\) (from \(C\) to \(A\)) and \(\overrightarrow{CB}\) (from \(C\) to \(B\)) are the two rays forming \(\angle 4\) at vertex \(C\), so this is correct.
• Option C: \(\overrightarrow{CD}\) is not a side of \(\angle 4\) (it goes to \(D\), not related to \(\angle 4\)’s formation), so incorrect.

Answer:

B. \(\overrightarrow{CA}\), \(\overrightarrow{CB}\)