Question

naming angles, sides of angles, and vertices
(a) name the vertex of ∠1.
(b) name the sides of ∠nmq.
and
(c) write two other names for ∠2.
and

Explanation:

Step1: Recall the definition of vertex

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

Step2: Recall the definition of sides of an angle

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

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 \(\angle2\), since the vertex is \(M\), and the other two points on the rays are \(Q\) and \(P\), two other names are \(\angle QMP\) and \(\angle PMQ\).

Answer:

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