Question

use the figure to identify another name for ∠3.
options:
o a) ∠acd
o b) ∠adc, ∠cda
o c) ∠acd, ∠acb
o d) ∠ade, ∠edc

Explanation:

Step1: Recall angle naming rules

An angle can be named by the vertex and two points on its sides, with the vertex in the middle. For \(\angle 3\), the vertex is \(D\), and the sides are \(DC\) and \(DA\).

Step2: Analyze each option

• Option A: \(\angle ACD\) has vertex \(C\), not \(D\), so incorrect.
• Option B: \(\angle ADC\) and \(\angle CDA\) both have vertex \(D\), with sides \(DC\) and \(DA\), matching \(\angle 3\).
• Option C: \(\angle ACD\) (vertex \(C\)) and \(\angle ACB\) (vertex \(C\)) are incorrect.
• Option D: \(\angle ADE\) and \(\angle EDC\) involve side \(DE\), not \(DA\) for \(\angle 3\), so incorrect.

Answer:

B) \(\angle ADC\), \(\angle CDA\)