Question

use the figure to complete each part. (a) name the vertex of ∠pmn. (b) write two other names for ∠qmp. (c) name the sides of ∠1.

Explanation:

Step1: Recall vertex definition

The vertex of an angle is the common - point where the rays forming the angle meet. For ∠PMN, the common point of rays $\overrightarrow{PM}$ and $\overrightarrow{MN}$ is M.

Step2: Recall angle - naming rules

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. For ∠QMP, other names are ∠2 (using the number assigned to the angle) and ∠PMQ (re - arranging the points with the vertex M in the middle).

Step3: Identify angle sides

The sides of an angle are the rays that form the angle. For ∠1, the rays are $\overrightarrow{MQ}$ and $\overrightarrow{MN}$.

Answer:

(a) M
(b) ∠2, ∠PMQ
(c) $\overrightarrow{MQ}$, $\overrightarrow{MN}$