Question

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

Explanation:

Part (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 \(\angle2\), the vertex is \(M\). Using three - point naming, we can write \(\angle PMQ\) (since \(P\), \(M\), \(Q\) are the points with \(M\) as the vertex). Also, since the vertex is \(M\) and there is no confusion (as the problem is about the given figure), we can use \(\angle M\) (but in a more precise three - point notation, another valid name is \(\angle QMP\))

Part (b)

Step1: Recall the definition of an angle's sides

The sides of an angle \(\angle NMQ\) are the two rays that form the angle. By the definition of an angle (a figure formed by two rays with a common endpoint), for \(\angle NMQ\) with vertex \(M\), the two rays are \(\overrightarrow{MN}\) and \(\overrightarrow{MQ}\)

Part (c)

Step1: Recall the definition of an angle's vertex

The vertex of an angle is the common endpoint of the two rays that form the angle. For \(\angle1\), the two rays that form the angle meet at the point \(M\)

Answer:

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