Question

in the diagram below, \\( \overline{da} \\) bisects \\( \angle bae \\) \\( \overline{ba} \parallel \overline{ce} \\), \\( \overline{cb} \parallel \overline{da} \\) and \\( \text{m}\angle c = 64^\circ \\). find \\( \text{m}\angle e \\).

step 1
angle: \\( \text{m}\angle c = 64^\circ \\)
reason: given

try \\( \text{m}\angle \square = \square^\circ \\)
select a reason

Explanation:

Step1: Find m∠DAB

Since $\overline{CB} \parallel \overline{DA}$ and $\overline{BA} \parallel \overline{CE}$, quadrilateral ABCD is a parallelogram. So $m\angle DAB = m\angle C = 64^\circ$.

Step2: Find m∠BAE

$\overline{DA}$ bisects $\angle BAE$, so $\angle BAE = 2 \times m\angle DAB = 2 \times 64^\circ = 128^\circ$.

Step3: Find m∠E

$\overline{BA} \parallel \overline{CE}$, so $\angle BAE + \angle E = 180^\circ$ (consecutive interior angles). Thus $m\angle E = 180^\circ - 128^\circ = 52^\circ$.

Answer:

52