use the figure to complete each part.
(a) write two other names for $ \angle 1 $.
$ \square $ and $ \square $
(b) name the sides of $ \angle 2 $.
$ \square $ and $ \square $
(c) name the vertex of $ \angle pmq $.
$ \square $

Question

Accepted Answer

# Explanation:
## Part (a)
### Step 1: Recall angle naming rules
An angle can be named by its vertex and two points on its sides, with the vertex in the middle, or by the vertex alone if there's no ambiguity. For $ \angle 1 $, the vertex is $ M $, and the sides have points $ N $ and $ Q $. So one name is $ \angle NMQ $, and another is $ \angle QMN $ (since the order of the side points can be reversed as long as the vertex is in the middle). Also, it can be named $ \angle M $ if there's no other angle at $ M $ that would cause confusion, but here with the sides $ MN $ and $ MQ $, the two other names using three points are $ \angle NMQ $ and $ \angle QMN $.

## Part (b)
### Step 1: Identify sides of $ \angle 2 $
The angle $ \angle 2 $ has vertex $ M $, and its sides are the rays forming it. Looking at the figure, the rays are $ MP $ (or $ PM $) and $ MQ $ (or $ QM $). So the sides are $ \overrightarrow{MP} $ (or $ \overrightarrow{PM} $) and $ \overrightarrow{MQ} $ (or $ \overrightarrow{QM} $).

## Part (c)
### Step 1: Recall vertex definition
The vertex of an angle is the common endpoint of the two rays forming the angle. For $ \angle PMQ $, the rays are $ \overrightarrow{PM} $ and $ \overrightarrow{QM} $, so their common endpoint is $ M $.

# Answers:
(a) $ \angle NMQ $ and $ \angle QMN $ (or $ \angle M $ if acceptable, but three - point names are more precise here)
(b) $ \overrightarrow{MP} $ and $ \overrightarrow{MQ} $ (or $ \overrightarrow{PM} $ and $ \overrightarrow{QM} $)
(c) $ M $

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step 1: Recall angle naming rules

Part (b)

Step 1: Identify sides of \( \angle 2 \)

Part (c)

Step 1: Recall vertex definition

Answer: