Question

(a) write two other names for ∠qmp.

(b) name the vertex of ∠pmn.

(c) name the sides of ∠1.

Explanation:

Step1: Recall angle - naming rules

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.

Step2: Answer part (a)

For $\angle{QMP}$, two other names are $\angle{2}$ and $\angle{PMQ}$ since the vertex is $M$ and the rays are $\overrightarrow{MP}$ and $\overrightarrow{MQ}$.

Step3: Answer part (b)

The vertex of $\angle{PMN}$ is the point $M$ as it is the common endpoint of the rays $\overrightarrow{PM}$ and $\overrightarrow{MN}$.

Step4: Answer part (c)

The sides of $\angle{1}$ are $\overrightarrow{MN}$ and $\overrightarrow{MQ}$ as these are the two rays that form the angle with vertex $M$.

Answer:

(a) $\angle{2}$ and $\angle{PMQ}$
(b) $M$
(c) $\overrightarrow{MN}$ and $\overrightarrow{MQ}$