Question

(d) problem 20: (first taught in lesson 31)
if ℓ || m, and de bisects ∠cdf, find y.
130°
after you enter your answer press go.
y =

Explanation:

Step1: Find $\angle CDF$

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

Step2: Use angle - bisector property

Since $\overrightarrow{DE}$ bisects $\angle CDF$, $\angle CDE=\frac{1}{2}\angle CDF$. Then $\angle CDE = 25^{\circ}$.

Step3: Find $y$

$\ell\parallel m$, and $\angle CDE$ and $y$ are alternate interior angles. So $y = 65^{\circ}$ (because the angle adjacent to the $25^{\circ}$ angle formed by the transversal and $\ell$ is $y$ and they are alternate interior angles with respect to the parallel lines $\ell$ and $m$).

Answer:

$65$