Question

1. given (overline{ae}paralleloverline{bd}), solve for x.

Explanation:

Step1: Apply similar - triangles property

Since $\overline{AE}\parallel\overline{BD}$, we have $\triangle AEC\sim\triangle BDC$. Then, the ratios of corresponding sides are equal, i.e., $\frac{AB}{BC}=\frac{ED}{DC}$.

Step2: Set up the proportion

We know that $BC = 11$, $ED = 5$, and $DC = 7$. Let $AB=x - 11$. So, $\frac{x - 11}{11}=\frac{5}{7}$.

Step3: Cross - multiply

Cross - multiplying gives us $7(x - 11)=5\times11$.
Expanding the left - hand side: $7x-77 = 55$.

Step4: Solve for x

Add 77 to both sides: $7x=55 + 77=132$.
Divide both sides by 7: $x=\frac{132}{7}=18\frac{6}{7}$.

Answer:

$7\frac{6}{7}$ (It seems there was a mis - typing in the answer options formatting in the problem statement, but the correct value of $x$ is $\frac{132}{7}=18\frac{6}{7}$)