Answer
$x = 63^{\circ}$
$y = 8$
Work Step by Step
In similar figures, corresponding angles are congruent, and corresponding sides are proportional. Each set of corresponding sides has the same ratio.
Let's look at the angles to figure out which one is congruent to $\angle x$. We see that the congruent angle in the other figure is the one that measures $63^{\circ}$. Therefore, $x = 63^{\circ}$.
Let's set up a proportion to set the ratios of sides equal to one another:
$\frac{4}{y} = \frac{8}{16}$
Use the cross products property to eliminate the fractions:
$8y = 64$
Divide each side of the equation by $8$ to solve for $y$:
$y = 8$
