Answer
$x=8
\\A=30^o
\\B=75^o
\\C=75^o$
Work Step by Step
RECALL:
Two similar triangles have:
(1) corresponding angles that are congruent; and
(2) corresponding sides that are proportional
Since corresponding angles are congruent, then
$A=30^o
\\B=75^o
\\C=75^o$
Corresponding sides of similar triangles are proportional.
Thus,
$\dfrac{12}{6}=\dfrac{16}{x}$
Cross-multiply to obtain:
$\begin{array}{ccc}
&12(x) &= &16(6)
\\&12x &= &96
\\&\frac{12x}{12} &= &\frac{96}{12}
\\&x &= &8\end{array}$
