Question

use the figure to complete each part. (a) write two other names for ∠1. and (b) name the sides of ∠2. and (c) name the vertex of ∠pmq.

Explanation:

Step1: Recall angle - naming rules

An angle can be named by its vertex and the two rays that form it, or just by its vertex if there is no confusion.

Step2: Answer part (a)

For $\angle1$, two other names are $\angle NMQ$ and $\angle QMN$ since the vertex is $M$ and the rays are $\overrightarrow{MN}$ and $\overrightarrow{MQ}$.

Step3: Answer part (b)

The sides of $\angle2$ are $\overrightarrow{MP}$ and $\overrightarrow{MQ}$ as these are the two rays that form the angle with vertex $M$.

Step4: Answer part (c)

The vertex of $\angle PMQ$ is the point where the two rays $\overrightarrow{MP}$ and $\overrightarrow{MQ}$ meet, which is point $M$.

Answer:

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