Question

use the figure to identify another name for ∠cad.
figure: points a, b, c, d, e with lines/arrows; angles labeled 1,2,3,4 at a, d, c, d respectively
options:
o a) ∠4, ∠acd
o b) ∠1, ∠dac
o c) ∠2, ∠dea
o d) ∠3, ∠edc

Explanation:

To name an angle, we can use the vertex and two points on the sides, or a number if labeled. For \( \angle CAD \), the vertex is \( A \), and the sides are \( AC \) and \( AD \). Looking at the labels, \( \angle CAD \) is also labeled as \( \angle 1 \) (using the number at the vertex) and can be named as \( \angle DAC \) (reversing the order of the points on the sides, since the middle letter is the vertex). Let's check the options:

• Option A: \( \angle 4 \) and \( \angle ACD \) refer to a different angle (at \( C \)), so incorrect.
• Option B: \( \angle 1 \) is the same as \( \angle CAD \) (since it's the angle at \( A \) between \( AC \) and \( AD \)), and \( \angle DAC \) is the same angle (vertex \( A \), sides \( DA \) and \( AC \)), so correct.
• Option C: \( \angle 2 \) and \( \angle DEA \) refer to angles at \( D \) and \( E \), incorrect.
• Option D: \( \angle 3 \) and \( \angle EDC \) refer to angles at \( D \), incorrect.

Answer:

B) \( \angle 1 \), \( \angle DAC \)