Question

in the diagram below, $overline{ab}paralleloverline{cd}$, $overline{ad}paralleloverline{bc}$, $\text{m}angle eab = 27^{circ}$ and $\text{m}angle dea = 60^{circ}$. find $\text{m}angle cde$.

Explanation:

Step1: Use alternate - interior angles

Since $\overline{AB}\parallel\overline{CD}$, $\angle EAB$ and $\angle ECD$ are alternate - interior angles. So, $m\angle ECD=m\angle EAB = 27^{\circ}$.

Step2: Consider the angle - sum property of a triangle

In $\triangle CDE$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. We know that $\angle DEC = 60^{\circ}$ (vertically opposite to $\angle DEA$) and $\angle ECD=27^{\circ}$. Let $m\angle CDE=x$. Then, by the angle - sum property of a triangle, $x + 27^{\circ}+60^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

$x=180^{\circ}-(27^{\circ} + 60^{\circ})=93^{\circ}$.

Answer:

$93^{\circ}$