Question

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

Explanation:

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 \(\angle1\), the common endpoint of its two rays is \(B\).

Step2: Recall the definition of the sides of an angle

The sides of an angle are the two rays that form the angle. For \(\angle ABC\), the two rays are \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\)

Step3: Recall the different ways to name an angle

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). For \(\angle2\), since its vertex is \(B\) and the other two points on its sides are \(C\) and \(D\), it can be named as \(\angle CBD\) or \(\angle DBC\)

Answer:

(a) \(B\)
(b) \(\overrightarrow{BA}\), \(\overrightarrow{BC}\)
(c) \(\angle CBD\), \(\angle DBC\)