Question

question
in the diagram below, (overline{ad} cong overline{ae}), (overline{ba} parallel overline{ce}), (overline{cb} parallel overline{da}) and (mangle bcd = 62^circ). find (mangle e).
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
answer attempt 1 out of 2
(mangle e=square^circ)
submit answer

Explanation:

Step1: Identify parallelogram properties

Since $\overline{BA} \parallel \overline{CE}$ and $\overline{CB} \parallel \overline{DA}$, $ABCD$ is a parallelogram. In a parallelogram, opposite angles are equal, so $m\angle BCD = m\angle BAD = 62^\circ$.

Step2: Find angle for parallel lines

$\overline{CB} \parallel \overline{DA}$, so $\angle BAD$ and $\angle ADE$ are corresponding angles, meaning $m\angle ADE = 62^\circ$.

Step3: Use isosceles triangle properties

$\overline{AD} \cong \overline{AE}$, so $\triangle ADE$ is isosceles with $\angle E = \angle ADE$.

Answer:

$62$