In the following figure,ray $BA$ is perpendicular to line $CD$. If $x: y: z = 4: 5: 6$,then find the values of $x, y,$ and $z$.

(N/A) Given that $AB \perp CD$,therefore $\angle ABC = 90^{\circ}$.
From the figure,$\angle ABC = x + y + z = 90^{\circ}$.
The ratio of the angles is given as $x : y : z = 4 : 5 : 6$.
Let the angles be $4k, 5k,$ and $6k$ respectively.
Sum of the ratios $= 4 + 5 + 6 = 15$.
Therefore,$15k = 90^{\circ}$,which gives $k = \frac{90^{\circ}}{15} = 6^{\circ}$.
Now,calculating the values:
$x = 4k = 4 \times 6^{\circ} = 24^{\circ}$
$y = 5k = 5 \times 6^{\circ} = 30^{\circ}$
$z = 6k = 6 \times 6^{\circ} = 36^{\circ}$
Thus,the values are $x = 24^{\circ}, y = 30^{\circ},$ and $z = 36^{\circ}$.