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:

Part (a)

• Step1: Recall angle - naming rules

An angle can be named using three points (vertex in the middle) or just the vertex (if there is no ambiguity). For \(\angle1\), the vertex is \(M\). Using three - point names: \(\angle NMQ\) (since the sides are \(MN\) and \(MQ\)). Another name is \(\angle QMN\) (order of non - vertex points can be interchanged as long as the vertex is in the middle).

Part (b)

• Step1: Identify the sides of an angle

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

Part (c)

• Step1: Recall the definition of the vertex of an angle

The vertex of an angle is the common endpoint of the two rays that form the angle. For \(\angle PMQ\), the common endpoint of rays \(MP\) and \(MQ\) is \(M\).

Answer:

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