1. The problem involves identifying angle names, vertices, and sides from a given figure with rays originating from point M. 2. (a) Two other names for \(\angle QMP\) are \(\angle PMQ\) and \(\angle M\) because angles can be named by three points with the vertex in the middle or just by the vertex if unambiguous. 3. (b) The vertex of \(\angle PMN\) is point \(M\) since the vertex is always the common endpoint of the rays forming the angle. 4. (c) The sides of \(\angle 1\) are the rays \(\overrightarrow{MN}\) and \(\overrightarrow{MQ}\) as the angle is formed between these two rays. Final answers: (a) \(\angle PMQ\) and \(\angle M\) (b) \(M\) (c) \(\overrightarrow{MN}\) and \(\overrightarrow{MQ}\)