Question

if $ellparallel m$, and $overrightarrow{de}$ bisects $angle cdf$, find $y$.

Explanation:

Step1: Find $\angle CDF$

Since $\ell\parallel m$, and the co - interior angle to the $130^{\circ}$ angle with respect to the transversal is $\angle CDF$. Co - interior angles are supplementary. So $\angle CDF = 180 - 130=50^{\circ}$.

Step2: Use the 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 $y$

$\ell\parallel m$, and $y$ and $\angle CDE$ are alternate interior angles. Alternate interior angles are equal. So $y = 65^{\circ}$.

Answer:

$65$