Question

(d) problem 20: (first taught in lesson 31) if ℓ || m, and de bisects ∠cdf, find y.

Explanation:

Step1: Find $\angle CDF$

Since $\ell\parallel m$, $\angle CDF = 130^{\circ}$ (corresponding - angles).

Step2: Use angle - bisector property

Since $\overrightarrow{DE}$ bisects $\angle CDF$, then $\angle CDE=\angle EDF=\frac{1}{2}\angle CDF$.
So $\angle CDE=\frac{1}{2}\times130^{\circ} = 65^{\circ}$.

Step3: Find $y$

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

Answer:

$65$