# The measure of angle DBE is (0.1x - 22)° and the measure of angle CBE is (0.3x - 54)°. Find the value of x.

Question
Performing transformations
The measure of \angle DBE is (0.1x - 22)° and the measure of \angle CBE is (0.3x - 54)°. Find the value of x.

2020-12-25
$$\displaystyle{m}\angle{D}{B}{E}+{m}\angle{C}{B}{E}={m}\angle{D}{B}{C}$$
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:
$$\displaystyle{0.4}{x}−{76}={90}$$
$$\displaystyle{0.4}{x}={166}$$
$$\displaystyle{x}={\frac{{{166}}}{{{0.4}}}}$$
$$\displaystyle{x}={415}$$

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