Question

use the figure and follow the directions below.

part 1 of 3
(a) name the sides of ∠1.

correct answer:
$overrightarrow{ba}$
$overrightarrow{bc}$

part 2 of 3
(b) name the vertex of ∠dba.

correct answer:
b

progress: 2/3

part 3 of 3
(c) write two other names for ∠cbd.

Explanation:

To name an angle, we can use the vertex in the middle with the two rays (sides) as the other points, or we can use the number if there is one. For \(\angle CBD\), the vertex is \(B\), and the sides are \(\overrightarrow{BC}\) and \(\overrightarrow{BD}\). So we can also name it by reversing the order of the rays (since the angle is between the same two rays) or using the number (if given, here \(\angle 2\) as seen in the figure).

Step 1: Identify the vertex and sides

The angle \(\angle CBD\) has vertex \(B\) and sides \(\overrightarrow{BC}\) and \(\overrightarrow{BD}\).

Step 2: Form other names

• Using the vertex in the middle with the sides reversed: \(\angle DBC\) (because the angle is between \(\overrightarrow{BD}\) and \(\overrightarrow{BC}\), so we can write the points as \(D\), \(B\), \(C\) with \(B\) as the vertex).
• Using the number: From the figure, \(\angle CBD\) is also labeled as \(\angle 2\), so \(\angle 2\) is another name.

Answer:

\(\angle DBC\) and \(\angle 2\)