Question

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

Explanation:

(a) Write two other names for ∠1

Step1: Recall angle - naming rules

An angle can be named using three points (vertex in the middle) or the vertex (if there is only one angle at the vertex). For ∠1, the vertex is \(M\). Using three - point naming:

• One name is \(\angle QMN\) (with \(M\) as the vertex).
• Another name is \(\angle NMQ\) (also with \(M\) as the vertex).

(b) Name the sides of ∠2

Step1: Identify the sides of an angle

The sides of an angle are the two rays that form the angle. For \(\angle2\), the rays are \(\overrightarrow{MP}\) and \(\overrightarrow{MQ}\).

(c) Name the vertex of ∠PMQ

Step1: Recall the vertex definition

The vertex of an angle is the common endpoint of the two rays forming the angle. For \(\angle PMQ\), the common endpoint of \(\overrightarrow{MP}\) and \(\overrightarrow{MQ}\) is \(M\).

Answer:

(a) \(\angle QMN\) and \(\angle NMQ\)
(b) \(\overrightarrow{MP}\) and \(\overrightarrow{MQ}\)
(c) \(M\)