Question

finding angles (level 1)
question
in the diagram below, \\(\overline{ad} \cong \overline{ae}\\), \\(\overline{ba} \parallel \overline{ce}\\), \\(\overline{cb} \parallel \overline{da}\\) and \\(\text{m}\angle dae = 52^\circ\\). find \\(\text{m}\angle bad\\).
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 bad = \square ^\circ\\)

Explanation:

Step1: Identify isosceles triangle

$\triangle ADE$ is isosceles since $\overline{AD} \cong \overline{AE}$.

Step2: Calculate base angles of $\triangle ADE$

Base angles are equal: $\angle AED = \angle ADE = \frac{180^\circ - 52^\circ}{2} = 64^\circ$

Step3: Use parallel lines property

Since $\overline{BA} \parallel \overline{CE}$, $\angle BAD = \angle ADE$ (alternate interior angles).

Answer:

$64$