Question

in the diagram below, \\(\overline{ad} \cong \overline{ae}\\), \\(\overline{ba} \parallel \overline{ce}\\), \\(\overline{cb} \parallel \overline{da}\\) and \\(\text{m}\angle bad = 62^\circ\\). find \\(\text{m}\angle dae\\).

you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

answer
attempt 1 out of 2
\\(\text{m}\angle dae = \square ^\circ\\)

Explanation:

Step1: Use parallel lines property

Since $\overline{BA} \parallel \overline{CE}$ and $\overline{AD}$ is a transversal, alternate interior angles are equal:
$\angle BAD = \angle ADE = 62^\circ$

Step2: Identify isosceles triangle

Given $\overline{AD} \cong \overline{AE}$, $\triangle AED$ is isosceles, so base angles are equal:
$\angle ADE = \angle AED = 62^\circ$

Step3: Calculate $\angle DAE$

Sum of angles in a triangle is $180^\circ$. Let $\text{m}\angle DAE = x$:
$$x + 62^\circ + 62^\circ = 180^\circ$$
$$x = 180^\circ - 124^\circ$$

Answer:

$56$