Question

in the diagram below, $overline{ab} \parallel \overline{cd}$, $overline{ad} \parallel \overline{bc}$, $\text{m}\angle eab = 30^\circ$ and $\text{m}\angle dea = 64^\circ$. find $\text{m}\angle cde$.

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

Explanation:

Step1: Find $\angle ADE$ in $\triangle ADE$

First, use the triangle angle sum theorem (sum of angles in a triangle is $180^\circ$).
$\angle ADE = 180^\circ - \angle EAB - \angle DEA = 180^\circ - 30^\circ - 64^\circ = 86^\circ$

Step2: Use parallel lines to find $\angle ADC$

Since $\overline{AB} \parallel \overline{CD}$, alternate interior angles are equal: $\angle ADC = \angle EAB = 30^\circ$

Step3: Calculate $\angle CDE$

$\angle CDE = \angle ADE - \angle ADC = 86^\circ - 30^\circ = 56^\circ$

Answer:

$56^\circ$