Question

practice
example 1
use the figure to identify angles and parts of angles that satisfy each given condition.

1. name the vertex of ∠1.
2. name the sides of ∠4.
3. what is another name for ∠3?

Explanation:

Step1: Recall angle - vertex definition

The vertex of an angle is the common endpoint of the rays that form the angle. For $\angle1$, the common endpoint of the rays is point $A$.

Step2: Recall angle - side definition

The sides of an angle are the two rays that form the angle. For $\angle4$, the rays are $\overrightarrow{CA}$ and $\overrightarrow{CD}$.

Step3: Recall angle - naming convention

An angle can be named by the vertex if there is only one angle at that vertex, or by three points with the vertex in the middle. $\angle3$ can also be named as $\angle ADE$ or $\angle EDA$ since the vertex is $D$ and the rays forming the angle pass through points $A$ and $E$.

Answer:

1. The vertex of $\angle1$ is $A$.
2. The sides of $\angle4$ are $\overrightarrow{CA}$ and $\overrightarrow{CD}$.
3. Another name for $\angle3$ is $\angle ADE$ or $\angle EDA$.