Question

use the figure to complete each part.
(a) name the vertex of \\( \angle p m q \\).
(b) name the sides of \\( \angle 2 \\).
and
(c) write two other names for \\( \angle 1 \\).
and

Explanation:

(a) Vertex of ∠PMQ

• Step1: Recall vertex definition

A vertex of an angle is the common endpoint of the two rays forming the angle. In ∠PMQ, the common endpoint of rays \(MP\) and \(MQ\) is \(M\).

(b) Sides of ∠2

• Step1: Identify angle components

An angle is formed by two rays. ∠2 is formed by rays \(MP\) and \(MQ\).

(c) Other names for ∠1

• 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). For ∠1, since the vertex is \(M\) and the rays are \(MN\) and \(MQ\), two other names are ∠NMQ and ∠QMN.

Answer:

(a) \(M\)
(b) \(MP\) and \(MQ\)
(c) \(∠NMQ\) and \(∠QMN\)