Question

if $ellparallel m$, and $overrightarrow{de}$ bisects $angle cdf$, find $y$. after you enter your answer press go. $y =$

Explanation:

Step1: Find $\angle CDF$

Since $\ell\parallel m$, $\angle CDF$ and the $130^{\circ}$ angle are same - side interior angles. Same - side interior angles are supplementary. So $\angle CDF = 180^{\circ}-130^{\circ}=50^{\circ}$.

Step2: Use angle - bisector property

Since $\overrightarrow{DE}$ bisects $\angle CDF$, then $\angle CDE=\angle EDF$. And $\angle CDE=\frac{1}{2}\angle CDF$. Substituting $\angle CDF = 50^{\circ}$, we get $\angle CDE = 25^{\circ}$.

Step3: Find $y$

$\angle CDE$ and $y^{\circ}$ are alternate interior angles. Alternate interior angles are congruent when two parallel lines are cut by a transversal. So $y = 65$.

Answer:

$65$