Question

Shown are two similar polygonsFind the values of x, y, and z.

Answer 1

Given:

The given two polygones are similar.

That means their corresponding angles and sides are congruent.

It gives,

$\begin{gathered} \frac{18}{16}=\frac{y}{18}=\frac{12}{x} \\ \frac{18}{16}=\frac{y}{18} \\ y=20.25 \\ \frac{18}{16}=\frac{12}{x} \\ x=10.7 \end{gathered}$

Also, we know the sum of all angles of triangle is 180 degree.

$\begin{gathered} 112^{\circ}+32^{\circ}+a^{\circ}=180^{\circ} \\ a^{\circ}=36^{\circ} \end{gathered}$

It gives,

$z^{\circ}=36^{\circ}$

Answer:

$\begin{gathered} x=10.7 \\ y=20.25 \\ z=36 \end{gathered}$