Question

your answer (a) name the vertex of ∠pmq. (b) name the sides of ∠2. (c) write two other names for ∠1.

Explanation:

Step1: Recall vertex definition

The vertex of an angle is the common - point where the two rays forming the angle meet. For $\angle PMQ$, the common point of rays $\overrightarrow{MP}$ and $\overrightarrow{MQ}$ is $M$.

Step2: Recall side - of - angle definition

The sides of an angle are the two rays that form the angle. For $\angle2$ (which is $\angle PMQ$), the sides are $\overrightarrow{MP}$ and $\overrightarrow{MQ}$.

Step3: Find alternative angle names

An angle can be named by the vertex alone (if there is no confusion) or by points on the rays and the vertex. For $\angle1$ (which is $\angle NMQ$), two other names are $\angle QMN$ and $\angle M$.

Answer:

(a) $M$
(b) $\overrightarrow{MP}$; $\overrightarrow{MQ}$
(c) $\angle QMN$; $\angle M$