Question

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

Explanation:

(a) Vertex of ∠1

Step1: Recall vertex definition

The vertex is the common endpoint of the rays forming the angle.
For ∠1, the common endpoint of its rays is \(M\).

(b) Sides of ∠NMQ

Step1: Recall angle - side definition

The sides of an angle are the two rays that form the angle.
For ∠NMQ, the two rays are \(\overrightarrow{MN}\) and \(\overrightarrow{MQ}\).

(c) Other names for ∠2

Step1: Use angle - naming conventions

An angle can be named by its vertex (if there is only one angle at that vertex) or by three points (with the vertex in the middle).
Since ∠2 has vertex \(M\), and the rays are \(\overrightarrow{MQ}\) and \(\overrightarrow{MP}\), two other names are \(\angle QMP\) and \(\angle PMQ\).

Answer:

(a) \(M\)
(b) \(\overrightarrow{MN}\) and \(\overrightarrow{MQ}\)
(c) \(\angle QMP\) and \(\angle PMQ\)