Question

(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:

Part (a)

Step1: Recall angle naming rules

An angle can be named by the vertex and a point on each ray, with the vertex in the middle, or by the number if labeled, or by the vertex alone (if unique). For $\angle QMP$, the vertex is $M$, and the rays are $MQ$ and $MP$. So another name can be $\angle PMQ$ (swapping the order of the non - vertex points) and $\angle 2$ (since it's labeled as 2).

Step1: Recall vertex definition

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

Step1: Identify $\angle 1$

$\angle 1$ is formed by two rays with a common vertex $M$. Looking at the diagram, the two rays forming $\angle 1$ are $MN$ and $MQ$.

Answer:

$\angle PMQ$ and $\angle 2$

Part (b)