\(\displaystyle{m}\angle{D}{B}{E}+{m}\angle{C}{B}{E}={m}\angle{D}{B}{C}\)

Since \(\displaystyle\angle{D}{B}{C}\) is a right angle as indicated by the square symbol, then \(\displaystyle{m}\angle{D}{B}{C}={90}°\). Hence,

\(\displaystyle{\left({0.1}{x}−{22}\right)}+{\left({0.3}{x}−{54}\right)}={90}\)

Solve for x:

\(\displaystyle{0.4}{x}−{76}={90}\)

\(\displaystyle{0.4}{x}={166}\)

\(\displaystyle{x}={\frac{{{166}}}{{{0.4}}}}\)

\(\displaystyle{x}={415}\)