Question

use the figure to complete each part.
(a) name the sides of ∠nmq.
and
(b) write two other names for ∠2.
and
(c) name the vertex of ∠1.

Explanation:

Part (a)

Step 1: Recall angle side definition

An angle's sides are the two rays forming it. For $\angle NMQ$, the vertex is \( M \), and the rays are \( \overrightarrow{MN} \) and \( \overrightarrow{MQ} \).

Step 2: Identify the sides

So the sides are \( \overline{MN} \) (or \( \overrightarrow{MN} \)) and \( \overline{MQ} \) (or \( \overrightarrow{MQ} \)).

Part (b)

Step 1: Recall angle naming rules

An angle can be named by vertex and two points (one on each ray), or by vertex if unique. For \( \angle 2 \), vertex is \( M \), rays are \( \overrightarrow{MQ} \) and \( \overrightarrow{MP} \).

Step 2: Find other names

So other names are \( \angle QMP \) and \( \angle PMQ \).

Part (c)

Step 1: Recall vertex definition

The vertex of an angle is the common endpoint of the two rays. For \( \angle 1 \), the common endpoint is \( M \).

Step 2: Identify the vertex

So the vertex is \( M \).

Answer:

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