Question

1. what is ef?

Explanation:

Step1: Identify similar - shaped polygons

The two polygons are similar since their corresponding angles are equal ($\angle W = \angle E=49^{\circ}$, $\angle X=\angle F = 99^{\circ}$, $\angle Y$ and the un - labeled angle in the second polygon, $\angle Z=\angle G = 116^{\circ}$).

Step2: Set up proportion

For similar polygons, the ratios of corresponding sides are equal. We can set up the proportion using the corresponding sides. Let's use the pair of sides $WX$ and $EF$. The ratio of corresponding sides of similar polygons gives us $\frac{WX}{EF}=\frac{WZ}{EG}$. We know that $WX = 27$ ft, $WZ = 28$ ft, and $EG = 12$ ft. Let $EF=x$. Then $\frac{27}{x}=\frac{28}{12}$.

Step3: Cross - multiply and solve for $x$

Cross - multiplying gives us $28x=27\times12$. So, $28x = 324$. Then $x=\frac{324}{28}=\frac{81}{7}\approx11.57$ ft.

Answer:

$\frac{81}{7}$ ft or approximately $11.57$ ft