Question

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

Explanation:

(a)

Step1: Recall angle - naming rules

An angle can be named by its vertex (when there is only one angle at that vertex) or by three points (with the vertex in the middle). For \(\angle QMP\), the vertex is \(M\). Another way is to use the number. Since \(\angle QMP=\angle2 + \angle1\), but if we consider the angle formed by rays \(MQ\) and \(MP\), we can also name it as \(\angle PMQ\) (using three - point notation with vertex \(M\)) and \(\angle2+\angle1\) (using the sum of adjacent angles).

(b)

Step1: Identify the vertex of an angle

The vertex of an angle is the common endpoint of the rays that form the angle. For \(\angle PMN\), the rays are \(MP\) and \(MN\), and their common endpoint is \(M\).

(c)

Step1: Recall the definition of an angle's sides

The sides of an angle are the two rays that form the angle. For \(\angle1\), the rays are \(MQ\) and \(MN\).

Answer:

(a) \(\angle PMQ\) and \(\angle2 + \angle1\)
(b) \(M\)
(c) \(MQ\) and \(MN\)