Question

use the figure to complete each part.
(a) name the sides of ∠1.
and
(b) name the vertex of ∠pmn.

(c) write two other names for ∠qmp.
and

Explanation:

Step1: Recall the definition of an angle's sides

An angle is formed by two rays with a common endpoint. For \(\angle1\), the two rays (sides) are \(MN\) and \(MQ\).

Step2: Recall the definition of an angle's vertex

The vertex of an angle is the common endpoint of the two rays forming the angle. For \(\angle PMN\), the common endpoint of rays \(MP\) and \(MN\) is \(M\).

Step3: Recall the different ways to name an angle

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 \(\angle QMP\), since the vertex is \(M\), other names are \(\angle2\) (using the number label) and \(\angle PMQ\) (using three - point notation).

Answer:

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