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 = 50^\circ\\). find \\(\text{m}\angle bcd\\).

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 bcd = \square ^\circ\\)
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Explanation:

Step1: Find base angles of $\triangle AED$

Since $\overline{AD} \cong \overline{AE}$, $\triangle AED$ is isosceles with $\angle E = \angle ADE$.
Sum of angles in a triangle is $180^\circ$, so:
$$\angle E = \angle ADE = \frac{180^\circ - 50^\circ}{2} = 65^\circ$$

Step2: Use parallel lines $\overline{CB} \parallel \overline{DA}$

Corresponding angles are equal, so $\angle BCD = \angle ADE$.
$$\angle BCD = 65^\circ$$

Answer:

$65$